PATENT ABSTRACT
The present invention relates to a method and system that provides hierarchical adaptability components to a wireless process control and/or automation network that increase system efficiency and reliability. The invention comprehends an intelligent and efficient process to design and operate a wireless process control and/or automation network while utilizing minimum system resources. In certain embodiments, path requirements are specified per usage class whereby minimum utilization of bandwidth, paths and hardware is allocated, while meeting plant environment requirements for services such as closed-loop regulatory and supervisory control, open-loop control, alerting, logging and remote monitoring.

PATENT DESCRIPTION
RELATED APPLICATIONS 
     The present application is a United States national phase application under 35 USC §371 of PCT/US09/42517 filed on May 1, 2009, which claims priority to U.S. Provisional Patent Application 61/049,682 filed on May 1, 2008, both of which are incorporated by reference in their entireties in the present application. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to wireless process control systems and methods, and more particularly to such systems and methods that include hierarchical adaptability to operate a wireless process control and/or automation network while utilizing minimum system resources. 
     2. Description of Related Art 
     The International Society of Automation (ISA) has established a Wireless Systems for Automation Standards Committee (ISA-SP100) tasked with defining wireless connectivity standards. The SP100 wireless standard for process automation systems is applicable to industries such as oil and gas, petrochemical, water/wastewater treatment and manufacturing. The SP100 standard is intended for use in the 2.4 GHz band, with data transfer at speeds up to 250 kilobytes per second within a 300 meter range. SP100 devices have relatively lower data rates and energy requirements than comparable wireless Local Area Networks (LAN), as they are intended to be low cost devices. 
     The SP100 protocol specifies different types of communications, categorized as “usage classes,” and increasing in criticality based upon decreasing numerical designation. “Class 0” communications include those categorized as critical for safety applications such as emergency shut-down systems, and are deemed always critical; “Class 1” is for closed-loop regulatory control, often deemed critical; “Class 2” is for closed-loop supervisory control, usually non-critical; “Class 3” is for open-loop control; “Class 4” is for alerting or annunciation; and “Class 5” is for data logging. Certain events, such as alarms, can have different classifications of service depending on the message type. 
     In general, devices in an SP100 system can be divided into three categories, commonly referred to as “tiers.” Tier  1  includes end devices, such as meters, remote terminal units, valves, sensors, tank level measuring devices, and the like, each of which is connected to a wireless end device. Wireless end devices (WEDs) can transmit to and receive from all other devices, but cannot route to other devices. Tier  2  includes wireless intermediate devices (WIDs), which transmit to and receive from all other devices, and route to other devices. Tier  3  includes wireless gateway devices (WGDs), which transmit to, receive from, and route between other devices, and also conduct high level applications including protocol translation and assignment of paths for source-destination pairs. As used herein, the components WEDs, WIDs and WGDs are also referred to as “nodes.” 
       FIG. 1A  is a schematic diagram of a known exemplary architecture for an SP100 Wireless Process Control System of the prior art. Connectivity between WEDs L 17  and L 13  and WGDs L 35  and L 31 , respectively, are illustrated, although as will be understood by one of ordinary skill in the art, connectivity is typically provided between all WEDs and a WGD at the Central Control Room (CCR). For example, L 17 -L 293 -L 292 -L 36 -L 35  is a path for the source-destination pair L 17 -L 35 , and L 292 -L 35  is one of the links within this path. 
     Devices in an SP100 wireless system are generally connected in the form of a mesh or star-mesh network. Connection between the various devices is performed through radio communications, for instance as specified by a Carrier Sense Multiple Access with Collision Avoidance (CSMA-CA) protocol or the like, and connections are established at a network layer and a Medium Access Control (MAC) layer. 
     In existing wireless process control and/or automation systems, every frame transmitted from WED to the CCR is treated the same, regardless of its usage class or criticality. The constraints are that the transmitted frames reach the CCR within specified maximum allowable end-to-end time delay and a specified frame error rate (FER). Commonly, all WIDs and WGDs route incoming traffic irrespective of the usage class, and without regard to a frame&#39;s status as an original transmission or a retransmission. Multiple paths between WEDs and the CCR are typically specified in a routing table for increased reliability of data frame transmission and receipt. Retransmission of frames occurs and is requested if the received frame is judged to be erroneous or no acknowledgment is received (i.e., timeout occurs). 
     While a large number of paths provide a certain degree of reliability, this topology increases the bandwidth requirements for the wireless spectrum, battery energy usage, and quantity and/or sophistication level of requisite hardware. In addition, channel contention often occurs due to high channel utilization, increased latency between the WEDs and CCR, and frame blocking. Therefore, diminishing returns result, such that an increase in the number of paths beyond a certain level will not significantly increase the reliability, thereby inefficiently using bandwidth, hardware and battery usage energy requirements. 
     Another commonly employed wireless process control and/or automation network has been recently developed as a derivative of the Highway Addressable Remote Transmitter (HART) Communication Foundation protocols, referred to generally as the HART® protocol. However, the wireless implementation of the HART® protocol has suffered some of the same drawbacks as the SP100 protocol, namely, battery usage and channel contention. 
     Therefore, a need exists for reliable and adaptable methods and systems to operate a wireless process control and/or automation network while utilizing minimum system resources. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a method and system that provides hierarchical adaptability components to a wireless process control and/or automation network that increase system efficiency and reliability. The invention comprehends an intelligent and efficient process to design and operate a wireless process control and/or automation network while utilizing minimum system resources. In certain embodiments, path requirements are specified per usage class whereby minimum utilization of bandwidth, paths and hardware is allocated while meeting plant environment requirements for services such as closed-loop regulatory and supervisory control, open-loop control, alerting, logging and remote monitoring. 
     In wireless systems having a large number of networked devices, efficient spectrum usage and delay minimizations are critical design and planning factors. Wireless process control and/or automation networks, including those operating under the ISA-SP100 protocol and/or the wireless HART® protocol, co-exist with other wireless systems operating in similar bands, e.g., 2.4 MHz, such as wireless LAN (including IEEE 802.11), BLUETOOTH™, ZIGBEE™, and the like. Efficient spectrum utilization in operation of a wireless process control and/or automation network in turn benefits other wireless systems utilizing the same frequency band. Accordingly, the present invention minimizes spectrum utilization by routing only frames and/or packets that meet one or more constraints. Paths are identified that meet the specified constraint(s). During operation, paths are discarded and/or replaced when they longer satisfy the constraint(s). 
     In addition, wireless process control and/or automation network are commonly deployed in harsh and classified areas, such as hazardous areas referred to as “Class 1, Division 1” and “Class 1, Division 2.” In these locations, flammable gas mixtures can be present. Many wireless control and/or automation devices in these environments are commonly battery-operated, mandating periodic battery replacement. Accordingly, reducing battery demand results in higher lifecycle, lower capital and operating costs, and reduced occurrences of worker access to these network devices in areas classified as hazardous. 
     In one method of operating a wireless process control and/or automation network according to the present invention, steps are carried out to select a minimum number of paths for one or more source-destination pairs. Potential paths between each source-destination pair are initially chosen. The reliabilities of each of the potential paths and/or the effective reliabilities of groups of paths are determined Paths or groups of paths that meet the minimum reliability requirements are identified by comparing the calculated reliabilities and/or effective reliabilities with minimum reliability requirements specified in a set of routing rules. Paths are selected from the identified reliable paths based on a minimum number of paths specified in the set of routing rules and assigned in a routing table. Paths or groups of paths above the specified minimum number of paths that meet the reliability requirements are discarded, i.e., not assigned in the routing table (as opposed to disabling the path), or assigned as alternate paths in the routing table. The paths that are discarded can be assigned in the future, for instance, if one of the previously assigned paths or alternate paths encounters excessive traffic and can no longer meet the requisite constraint(s) including the minimum reliability requirements. 
     In another method of operating a wireless process control and/or automation network according to the present invention, steps are carried out to select paths based on constraints related to end-to-end delays between a source-destination pair. 
     In a further method of operating a wireless process control and/or automation network according to the present invention, steps are carried out to select paths based on constraints related to tier delays for links within a given tier. Notably, employing a constraint based on tier delays minimizes the number of links or hops in a given path between a source-destination pair. 
     In an additional method of operating a wireless process control and/or automation network according to the present invention, steps are carried out to select a minimum number of reliable paths that further meet constraints related to end-to-end delays and/or tier delays. 
     In still another method of operating a wireless process control and/or automation network according to the present invention, steps are carried out to select a minimum number of reliable paths that further meet constraints related to one or more of end-to-end delays and/or tier delays, maximum throughput per link, and a minimal number of hops. 
     In one system of the invention for operating a wireless process control and/or automation network, a route optimization module is executed by hardware which can include one or more of the wireless gateway devices, a separate computing device in communication with the wireless network, or a combination thereof. The route optimization module includes a path determination sub-module that determines possible paths between the selected source-destination pair. A reliability calculation sub-module is provided that determines the reliability of each of the possible paths, and/or the effective reliability of one or more groups of paths. The route optimization module also includes a reliable path identification sub-module that identifies reliable paths or groups of paths by comparing the reliability and/or effective reliability with minimum reliability requirements specified in a set of routing rules, and a path assignment sub-module for assigning reliable paths or one or more groups of paths to a routing table based on the a minimum number of paths specified in the set of routing rules. Paths or groups of paths above the specified minimum number of paths that meet the reliability requirements are discarded, i.e., not assigned in the routing table, or assigned as alternate paths in the routing table. 
     In another system of the invention for operating a wireless process control and/or automation network, an end-to-end delay minimization module is provided, in which paths are selected based on constraints related to end-to-end delays for paths between a source-destination pair. 
     In a further system of the invention for operating a wireless process control and/or automation network, a tier delay minimization module is provided, in which paths are selected based on constraints related to tier delays for links within a given tier. 
     In an additional system of the invention for operating a wireless process control and/or automation network, a delay minimization module is provided, in which paths are selected based on constraints related to both end-to-end delays and tier delays. 
     In still another system of the invention for operating a wireless process control and/or automation network, a module is provided to select a minimum number of reliable paths, and one or more additional or sub-modules modules are to select paths based on further constraints related to end-to-end delays and/or tier delays, maximum throughput per link, a minimal number of hops, or a combination of one or more of end-to-end delays and/or tier delays, maximum throughput per link, and a minimal number of hops. 
     In certain embodiments, the reliability, e.g., the maximum allowable frame error rate (FER), is specified for one or more of the usage classes, and the assigned minimum number of reliable paths is specified per usage class. Usage classes or groups of usage classes with higher degrees of criticality, e.g., classes 0 and 1 in an SP100 system, have a higher reliability threshold, i.e., lower maximum allowable frame error rates as compared to usage classes of lower criticality. Further, usage classes of lower criticality can have fewer assigned minimum reliable paths. 
     Further embodiments of the process of the present invention provide that the maximum allowable frame error rate per usage class, the process control wireless traffic distribution, the links&#39; reliability profile, tier delay, or a combination of these factors are used to generate a subset of paths containing a minimum number of paths with associated reliability weight. For source-destination pairs in which the minimum number of paths is not attained based on the above-described routing assignment process or the above-described sub-modules, selective paths are combined, i.e., groups of paths, or additional paths are incorporated, until the end-to-end frame error rate for each usage class is lower than the class&#39;s maximum allowable threshold, while applying the criteria of employing a minimum number of intermediate links. 
     Embodiments of the present invention include additional steps or sub-modules for incorporation within conventional wireless network protocols, including: (1) defining a maximum allowable delay for each tier; (2) including usage class bits to the routing table; (3) considering whether a frame is a retransmit frame; (4) providing an action-type bit to the frame format structure where the received frames for a destination are not actioned until the end of the maximum allowable delay (i.e., the received frame is not actioned until the end of the maximum allowable delay to ensure that all frames arriving from different routes are received and the frames with a high quality indicator are passed to the CCR for action); (5) dropping and/or routing the frame as a function of the usage class; and/or (6) during abnormal channel conditions, sending a control message to WIDs and/or WGDs in a wireless process control and/or automation protocol network to allow routing of frames for a particular pair of source-destination pairs irrespective of the usage class, thereby dynamically increasing the number of available paths. Accordingly, in certain embodiments, the method and system of the present invention minimizes the required number of frames transported over wireless links while meeting reliability and latency requirements. 
     In an example described below, it is demonstrated that by using the system and method of the present invention, (1) the battery lifecycle of hardware in an SP100 network is extended by more than 60%; (2) the cost of an SP100 system is significantly reduced due to reduction in the required number of WIDs and WGDs; and (3) spectrum utilization is reduced by at least 55%. These benefits are accomplished while maintaining the design requirements for plant applications such as closed-loop regulatory and supervisory control, open-loop control, alerting, and remote monitoring/logging. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing summary, as well as the following detailed description of preferred embodiments of the invention will be best understood when read in conjunction with the attached drawings. For the purpose of illustrating the invention, there are shown in the drawings embodiments which are presently preferred. It should be understood, however, that the invention is not limited to the precise arrangements and instrumentalities shown. In the drawings the same numeral is used to refer to the same or similar elements or steps, in which: 
         FIG. 1A  is a schematic diagram of a wireless process control and/or automation network architecture; 
         FIG. 1B  is a schematic diagram of a wireless process control and/or automation network architecture in accordance with the present invention; 
         FIG. 2  is a schematic diagram of architecture of a wireless process control and/or automation network according to certain embodiments of the present invention; 
         FIGS. 3A ,  3 B and  3 C are schematic diagrams of a wireless end device, a wireless intermediate device and a wireless gateway device used in conjunction with the system and method of the present invention; 
         FIG. 4  is a block diagram of a basic computing device configuration in accordance with embodiments of the present invention; 
         FIG. 5  is a schematic block diagram including a route optimization module in accordance with an embodiment of the present invention; 
         FIG. 6  is a flow chart of a method of assigning reliable paths for an source-destination pair in accordance with the present invention; 
         FIG. 7  is a schematic block diagram including an end-to-end delay minimization module in accordance with an embodiment of the present invention; 
         FIG. 8  is a flow chart of a method of assigning paths operating the end-to-end delay minimization module in accordance with the present invention; 
         FIG. 9  is a schematic block diagram including a tier delay minimization module in accordance with an embodiment of the present invention; 
         FIG. 10  is a flow chart of a method of assigning paths operating the tier delay minimization module in accordance with the present invention; 
         FIG. 11  is a schematic block diagram including a delay minimization module in accordance with an embodiment of the present invention; 
         FIG. 12  is a flow chart of a method of assigning paths operating the delay minimization module in accordance with the present invention; 
         FIG. 13  is a schematic diagram of a portion of a wireless process control and/or automation network architecture depicting a set of source-destination pair components; 
         FIG. 14  is a chart of normalized power usage comparison for wireless intermediate devices using the system and method of the present invention compared to prior art methods; and 
         FIG. 15  is a chart of normalized power usage comparison for wireless end devices and wireless gateway devices using the system and method of the present invention compared to methods of the prior art. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1B  is a diagram of a wireless process control and/or automation network such as one following the ISA-SP100 protocol; only connectivity for WEDs L 17  and L 13  to WGDs L 35  and L 31 , respectively, is illustrated. The path L 17 -L 293 -L 292 -L 36 -L 35  is one of the paths of the source-destination pair of L 17  and the central control room (CCR). The combination L 292 -L 35  is considered one of the links within this path. The path L 17 -L 291 -L 28 -L 34 -L 35  is a path independent from L 17 -L 293 -L 292 -L 36 -L 35 , since no single intermediate link is common to the two paths. Elements L 11  through L 17  are WEDs at tier  1 ; elements L 21  through L 29  and L 291  through L 293  are WIDs at tier  2 ; and elements L 31  through L 36  are WGDs at tier  3 . In the architecture shown in  FIG. 1 , the WGD L 31  at the CCR is referred to as a master WGD, and the other WGDs L 32  through L 36  are additional WGDs that can provide additional links and/or serve as backup gateway devices in the event that the master WGD fails. In accordance with the present invention, a computing device  80  is provided that executes the route optimization module  110 , the end-to-end delay minimization module  210 , the tier delay minimization module  310 , the delay minimization module  410 , other modules that apply constrains including one or more of throughput and number of hops, or a combination including at least one of the foregoing modules, to create the routing table  190 , and downloads the resulting routing table  190  to the routing WIDs and WGDs. 
       FIG. 2  shows an exemplary architecture  10  of a wireless process control and/or automation system. The architecture generally follows the Open Systems Interconnection Reference Model (OSI model), and includes: an application layer  12 , a transport layer  14 , a network layer  16 , data link layer  18  including a logical link control sublayer  20  and a media access control sublayer  22 , and a physical layer  24 . The application layer  12  includes the functionality of presentation and session layers according to a wireless process control and/or automation protocol such as the ISA-SP100 protocol, and generally provides the interface to user application processes. The application layer  12  further includes an application sublayer  26  that provides a wireless process control and/or automation protocol interface. The transport layer  14  provides for the addressing of user application processes via selection of a specific application layer entity. The network layer  16  provides network-wide addressing of devices and relays messages between network layer entities of different devices. Furthermore, in accordance with embodiments of the present invention, the network layer supports frame routing between source-destination pairs based upon the route optimization module  110  of the present invention. The data link layer  18  generally manages use of the physical layer, and includes the logical link control (LLC) sublayer  20  and the medium access control (MAC) sublayer  22 , and can also carry out some of the optimization functionalities in adaptive methods and systems of the present invention, such as collecting frame error rate data, throughput data and/or delay statistics, and passing that data to the route optimization module  110 . The LLC sublayer  20  provides multiplexing and flow control mechanisms, and generally acts as an interface between the MAC sublayer  22  and the network layer  16 . The MAC sublayer provides multiple access methods including the carrier sense multiple access with collision avoidance (CSMA-CA) protocol  28  commonly used in wireless networks, which is also carried out in the physical layer  24 . Finally, the physical layer  24  provides bit-by-bit delivery of data, a standardized interface transmission media including radio interfacing, modulation, and physical network topology such as mesh or star networks. In addition, channels assignments and/or changes are carried out in the network layer  24  and the data link layer  18 . 
       FIG. 3A  shows a block diagram of a WED  30  for receiving data from, and transmitting data to, one or more networked WIDs and/or WGDs. WED  30  generally includes a processor  32 , such as a central processing unit, a wireless transceiver  34  and associated antenna  36 , an input/output interface  40 , a clock  45  and support circuitry  42 . The processor  32 , wireless transceiver  34 , input/output interface  40 , clock  45  and support circuitry  42  are commonly connected via a bus  44 , which also connects to a memory  38 . Memory  38  can include both volatile (RAM) and non-volatile (ROM) memory units, and stores software or firmware programs in a program storage portion and stores data in a data storage portion. The input/output interface  40  sends and receives information via a communication link to and from the associated end devices  46 , e.g., process equipment such as meters, remote terminal units, valves, sensors, tank level measuring devices, and the like. The WED  30  can transmit to and receive from all other devices. In a receiving mode, the WED  30  receives instructions via the antenna  32  and transceiver  34 . These instructions are processed by the processor  32  and can be stored in memory  38  for later use or cached. A timestamp is preferably added to the data with the clock  45 , or alternatively, with a global positioning system. All devices in the network are synchronized to allow for accurate delay calculations as described below. The instructions are conveyed to the end device via the port  40 . In a transmission mode, data is conveyed from the end device to the port  40 , and passed to memory  38 . The data can be processed by the processor  36  including a timestamp generated by clock  45  or other means, and sent across the network through the transceiver  34  and antenna  32 . The processor  32  generally operates using the OSI model described above for end devices, and carries out instructions for transmission and receipt of data. 
       FIG. 3B  shows a block diagram of a WID  50  for transmitting to and receiving from all other devices, and for routing to other devices. WID  50  generally includes a processor  52 , such as a central processing unit, a wireless transceiver  54  and associated antenna  56 , a clock  65  and support circuitry  62 . The processor  52 , wireless transceiver  54 , clock  65  and support circuitry  62  are commonly connected via a bus  64 , which also connects to a memory  58 . Memory  58  commonly can include both volatile (RAM) and non-volatile (ROM) memory units, and stores software or firmware programs in a program storage portion and stores data in a data storage portion. A routing table  190  specified in accordance with the present invention resides in memory  58 , i.e., in the data storage portion. In a receiving mode, the WID  50  receives data frames via the antenna  56  and transceiver  54 . The data is generally cached in memory  58 , for instance, for transmission when specified by the CSMA-CA protocol, or for retransmission in the event of a failed frame transmission. In a transmission mode, data is conveyed from the memory to the transceiver  54  under control of the processor  52 . In a receiving mode, the WID  50  receives data frames via the antenna  56  and transceiver  54 . In a routing mode, data frames are received and transmitted. The clock  65  or other means such as a global positioning system can add timestamps to received, transmitted and/or routed data. The WID  50  has sufficient intelligence to be able to address and route to specific communication devices. The processor  52  generally operates using the OSI model described above for intermediate devices, and carries out instructions for transmission, receipt and routing of data. 
       FIG. 3C  shows a block diagram of a WGD  70  for transmitting to and receiving from all other devices, for routing to other devices, and in certain embodiments of the present invention for conducting high level applications including protocol translation and assignment of paths for source-destination pairs. WID  70  generally includes a processor  72 , such as a central processing unit, a wireless transceiver  74  and associated antenna  76 , a clock  85  and support circuitry  82 . The processor  72 , wireless transceiver  74 , clock  85  and support circuitry  82  are commonly connected via a bus  84 , which also connects to a memory  78 . Memory  78  commonly can include both volatile (RAM) and non-volatile (ROM) memory units, and stores software or firmware programs in a program storage portion and stores data in a data storage portion. A routing table  190  specified in accordance with the present invention resides in memory  78 , i.e., in the data storage portion. Furthermore, in certain embodiments of the present invention, the program storage portion of the memory  78  can include a routing optimization module  110  and a set of routing rules  120 . In receiving, transmission and routing modes, the WGD  70  operates in a manner similar to the operation of the WID  50 . The processor  72  generally operates using the OSI model described above for gateway devices, and carries out instructions for transmission, receipt and routing of data. The WGD  70  has sufficient intelligence to be able to address and route to specific communication devices. In addition, in certain embodiments of the present invention, the processor  72  of the WGD  70 , in particular a master WGD  70  executes the logic for the route optimization module  110 , the end-to-end delay minimization module  210 , the tier delay minimization module  310 , the delay minimization module  410 , other modules that apply constrains including one or more of throughput and number of hops, or a combination including at least one of the foregoing modules, and the path assignments are stored in the routing table  190 . In embodiments where the route optimization module and associated logic is carried out in other computing devices, the routing table  190  can be downloaded directly to the WIDs and WGDs for use during data routing operations, or transmitted through the wireless network in data frames and stored where required, i.e., in the routing WIDs and WGDs. 
     In certain embodiments of the present invention, the tier containing the WIDs can be bypassed, such that the WEDs transmit to, and receive from, WGDs. For instance, such a configuration is common in a wireless HART® protocol. In additional embodiments, WIDs can transmit frames to, and receive frames from, other WIDs, for instance, whereby WGDs are bypassed. 
     The following definitions and symbols are used herein to facilitate the description of the route optimization module and associated system and method of the present invention: 
     i denotes usage class as described above, and can be 0, 1, 2, 3, 4 or 5; 
     j denotes the tier of the wireless device and can be 1, 2 or 3; 
     D i  denotes the traffic distribution, i.e., percentage of the total traffic, for class i; 
     N P  denotes the number of possible paths between a source and a destination; 
     N i   opt  denotes the minimum number of paths for a source-destination pair in usage class i; 
     x denotes the path number, i.e. x=1, 2, 3, . . . , N P ; e.g., x=5 mean the 5 th  path out of N P  paths; 
     |L(x)| denotes the number of intermediate links for the x-th path; 
     |L i   opt | denotes the maximum number of intermediate links for a path for a source-destination pair in usage class i; 
     L(x, y) denotes the y-th link of the x-th path, for y=1, 2, 3, . . . , |L(x)|; 
     Φ(L(x, y)) denotes the frame error probability for the y-th link of the x-th path, and the link reliably profile is a matrix consisting of all [1−Φ(L(x, y))]; 
     Φ(x) denotes the frame error probability for the x-th path, e.g., Φ(2) is the frame error probability of path 2, Φ(2,5) is the effective frame error probability for the combined path 2 and 5; 
     1−Φ c (i) denotes the end-to-end reliability requirements for class i; 
     Φ c (i) denotes the end-to-end frame error probability requirements for class i; 
     α denotes the maximum allowable frame error probability for a single link; 
     η(L(x, y)) is the existing throughput for the y-th link of the x-th path; 
     η(L(x, y), max) is the maximum throughput for the y-th link of the x-th path; 
     ψ(j, i, x) denotes the calculated delay in tier j for class i going through path x, and the tier delay profile is a matrix for all ψ(j, i, x); 
     ψ(i, j, max) denotes the maximum allowable delay in tier j for class i; 
     ψ(i, x) denotes the calculated delay for a particular path x for class i; and 
     ψ(i, max) denotes the maximum allowable end-to-end delay for class i. 
     Table 1 represents process control system requirements based upon each usage class: 
     
       
         
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 Traffic 
                 Reliability 
                   
               
               
                 Class 
                   
                 Distribution 
                 Requirements 
                 Delay Requirements 
               
               
                 (i) 
                 Class Description 
                 D i   
                 1 − Φ c (i) 
                 ψ(i, j, max), ψ(i, max) 
               
               
                   
               
             
             
               
                 0 
                 Safety &amp; Emergency Actions 
                 D 0   
                 1 − Φ c (0) 
                 ψ(0, j, max), ψ(0, max) 
               
               
                 1 
                 Closed-Loop Regulatory Control 
                 D 1   
                 1 − Φ c (1) 
                 ψ(1, j, max), ψ(1, max) 
               
               
                 2 
                 Closed-Loop Supervisory Control 
                 D 2   
                 1 − Φ c (2) 
                 ψ(2, j, max), ψ(2, max) 
               
               
                 3 
                 Open-Loop Control 
                 D 3   
                 1 − Φ c (3) 
                 ψ(3, j, max), ψ(3, max) 
               
               
                 4 
                 Alerting 
                 D 4   
                 1 − Φ c (4) 
                 ψ(4, j, max), ψ(4, max) 
               
               
                 5 
                 Logging 
                 D 5   
                 1 − Φ c (5) 
                 ψ(5, j, max), ψ(5, max) 
               
               
                   
               
             
          
         
       
     
     The following description and related equations set forth an exemplary process and route optimization module for determining and assigning one or more reliable paths for a source-destination pair. However, one of ordinary skill in the art will appreciate that deviations from the set of equations that follow, including variations in sequence and precise definition of terms, can result in the same or an equivalent determination and assignment. Accordingly, in accordance with an embodiment of the present invention, the method steps described with respect to  FIGS. 5 and 6 ,  FIGS. 7 and 8 ,  FIGS. 9 and 10 ,  FIGS. 11 and 12 , and variations thereof, are implemented as a module, or set of instructions, in a computing device, which can include a WGD or a separate computing device. In the case of the module being executed by a WGD, the module can be executed in a master wireless gateway device, for instance, located in the CCR, or alternatively by one or more of the additional wireless gateway devices within tier  3 . 
     In embodiments in which the one or more modules  110 ,  210 ,  310 ,  410  are executed by a separate computing device, the end results, i.e., the assignment and determination of one or more reliable paths between a selected source-destination pair, can be ascertained and uploaded to one or more of the wireless gateway devices. In certain embodiments employing a separate computing device, an adaptive system is provided whereby communication between the separate computing device and one or more WGDs is maintained continuously (wired or wireless). In an adaptive system, one or more WGDs can be programmed to look to the separate computing device to determine and assign new paths between one or more selected source-destination pairs. In alternative embodiments, the WGDs and WIDs can communicate with the separate computing device periodically to receive updates. In further alternative embodiments, one or more WGDs and/or WIDs can instruct the separate computing device to execute the route optimization module of the present invention to alter assignments when performance degradation is detected, for example, in the case of one or more bad links or nodes within the wireless process control and/or automation network. 
     An exemplary block diagram of a computer system  80  in which the route optimization module of the present invention can be implemented is shown in  FIG. 4 . Computer system  80  includes a processor  82 , such as a central processing unit, an input/output interface  90  and support circuitry  92 . In certain embodiments, where the computer  80  requires a direct human interface, a display  96  and an input device  98  such as a keyboard, mouse or pointer are also provided. The display  96 , input device  98 , processor  82 , and support circuitry  92  are shown connected to a bus  94  which also connects to a memory  98 . Memory  98  includes program storage memory  111  and data storage memory  191 . Note that while computer  80  is depicted with direct human interface components display  96  and input device  98 , programming of modules and exportation of data can alternatively be accomplished over the interface  90 , for instance, where the computer  80  is connected to a network and the programming and display operations occur on another associated computer, or via a detachable input device as is known with respect to interfacing programmable logic controllers. 
     Program storage memory  111  and data storage memory  191  can each comprise volatile (RAM) and non-volatile (ROM) memory units and can also comprise hard disk and backup storage capacity, and both program storage memory  111  and data storage memory  191  can be embodied in a single memory device or separated in plural memory devices. Program storage memory  111  stores software program modules and associated data, and in particular stores a route optimization module  110 , the end-to-end delay minimization module  210 , the tier delay minimization module  310 , the delay minimization module  410 , other modules that apply constrains including one or more of throughput and number of hops, or a combination including at least one of the foregoing modules. Data storage memory  191  stores a set of routing rules  120  and a routing table  190  generated by the one or more modules of the present invention. 
     It is to be appreciated that the computer system  80  can be any computer such as a personal computer, minicomputer, workstation, mainframe, a dedicated controller such as a programmable logic controller, or a combination thereof. While the computer system  80  is shown, for illustration purposes, as a single computer unit, the system may comprise a group/farm of computers which can be scaled depending on the processing load and database size. In addition, as described above, the functionality of the computer system  80  can be executed by one or more of the WGDs. 
     The computing device  80  preferably supports an operating system, for example stored in program storage memory  111  and executed by the processor  82  from volatile memory. According to an embodiment of the invention, the operating system contains instructions for interfacing the device  80  to the wireless process control and/or automation network, including the route optimization module of the present invention as more fully discussed herein. 
       FIG. 5  is a schematic block diagram of a wireless process control and/or automation network routing system  100  according to an embodiment of the present invention. In general, the wireless process control and/or automation network routing system  100  includes a route optimization module  110 , a set of routing rules  120 , e.g., in the form of a routing table, and hardware  80  for executing the route optimization module  110  based on the set of routing rules  120 . In general, the route optimization module  110  is executable by suitably interconnected hardware  80 , such as one or more wireless gateway devices  80   a , a separate computing device  80   b , a combination of one or more wireless gateway devices  80   a  and a separate computing device  80   b , or other known processing device. 
     The set of routing rules  120  is commonly in the form of a rule table, although one of ordinary skill in the art of computer science will appreciate that the set of rules can be in a format other than a table, e.g., a database, a directory, or other type of file structure. The set of routing rules  120  in the form of a rule table includes a source column  122 , a destination column  124 , a usage class column  126 , a minimum reliability requirement 1−Φ c (i) column  128  and a column  130  specifying the minimum number of paths N i   opt  in a source-destination pair per usage class. In general, the rules are specified for end-to-end source-destination pairs, although in certain embodiments it can be desirable to specify rules for other source-destination pairs. For example, a destination WGD can be provided with communication to the CCR outside of the route optimization module  110  of the present invention. The route optimization module  110  uses this set of routing rules  120  in the for certain steps or sub-modules as described further herein. The set of routing rules  120  can be stored in the hardware  80 , or in a separate and accessible computer memory device, depending, for instance, upon the desired system configuration. 
     Still referring to  FIG. 5 , and also referring to  FIG. 6 , the operation of an embodiment of the route optimization module  110  is shown in more detail. A path determination sub-module  150  determines at step  152  possible paths between a selected source-destination pair. For example, referring to  FIG. 1 , for the source-destination pair of the wireless end device L 17  and the wireless gateway device L 35 , the paths shown by dashed lines include: 
     (i) L 17 -L 293 -L 292 -L 36 -L 35 ; 
     (ii) L 17 -L 293 -L 29 -L 36 -L 35 ; 
     (iii) L 17 -L 293 -L 29 -L 34 -L 35 ; and 
     (iv) L 17 -L 291 -L 292 -L 36 -L 35 ; 
     (v) L 17 -L 291 -L 292 -L 34 -L 35 ; 
     (vi) L 17 -L 291 -L 28 -L 34 -L 35 ; 
     (vii) L 17 -L 293 -L 292 -L 291 -L 28 -L 34 -L 35 ; 
     (viii) L 17 -L 291 -L 292 -L 293 -L 29 -L 36 -L 35 ; 
     (ix) L 17 -L 291 -L 292 -L 293 -L 29 -L 34 -L 35 . 
     For the source-destination pair of the wireless end device L 13  and the wireless gateway device L 31  at the central control room, the paths shown by dashed lines include: 
     (i) L 13 -L 23 -L 24 -L 32 -L 31 ; 
     (ii) L 13 -L 23 -L 32 -L 31 ; 
     (iii) L 13 -L 24 -L 23 -L 32 -L 31 ; 
     (iv) L 13 -L 24 -L 32 -L 31 ; 
     (v) L 13 -L 24 -L 25 -L 32 -L 31 ; 
     (vi) L 13  L 24  L 25  L 26  L 32  L 31 ; 
     (vii) L 13 -L 25 -L 32 -L 31 ; 
     (viii) L 13 -L 26 -L 32 -L 31   
     (ix) L 13 -L 25 -L 24 -L 32 -L 31   
     (x) L 13 -L 26 -L 25 -L 32 -L 31 ; and 
     (xi) L 13  L 26  L 25  L 24  L 32  L 31 . 
     Note that while paths show that data frames generally hop from a tier  1  node to one or more tier  2  nodes, and then to one or more tier  3  nodes, in certain embodiments a path can include data frames that hop from a tier  2  node to a tier  3  node, back to a tier  2  node and back to a tier  3  node, whereby duplication of nodes within a path is generally avoided. However, as described further herein, such paths having a larger number of hops will likely be eliminated from consideration in preferred embodiments of the present invention. Of course, one of ordinary skill in the art will recognize that other paths not specifically marked in  FIG. 1  are possible. 
     Next, a reliability calculation sub-module  160  calculates at step  162  the reliability of each of the possible paths, calculated from a link reliability profile. In certain alternative embodiments, the listing of all of the paths can be preliminarily filtered to eliminate those that are greater than a maximum number of links for a given usage class i, |L i   opt |. For example, if |L i   opt | is specified as five for all usage classes, an excessive path link filter sub-module can be applied to discard from the routing table  190  paths with more than five links, i.e., |L(x)|&gt;|L i   opt |, such as paths (vii), (viii) and (ix) of the source-destination pair of the wireless end device L 17  and the wireless gateway device L 35 . Likewise, an excessive path link filter sub-module can be applied to discard from the routing table  190  paths (vi) and (xi) related to the source-destination pair of the wireless end device L 13  and the wireless gateway device L 31 . 
     In additional and/or alternative embodiments, as described further herein, the link reliability profile data can be obtained from empirical data of frame error rates of each link, or derived from estimates calculated based upon the type of hardware and network loading. For instance, an exemplary profile of link FER values is given in Table 2 below: 
     
       
         
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                 Link FER 
               
               
                 Source 
                 Destination 
                 Φ(L(x, y)) 
               
               
                   
               
             
             
               
                 L13 
                 L23 
                 1.00E−05 
               
               
                 L13 
                 L24 
                 1.00E−06 
               
               
                 L13 
                 L25 
                 5.00E−07 
               
               
                 L13 
                 L26 
                 1.00E−07 
               
               
                 L23 
                 L32 
                 5.00E−04 
               
               
                 L24 
                 L32 
                 5.00E−06 
               
               
                 L25 
                 L32 
                 5.00E−04 
               
               
                 L26 
                 L32 
                 5.00E−03 
               
               
                   
               
             
          
         
       
     
     The reliability 1−Φ(x) for a path x is calculated from the link reliability profile data in Table 2 as follows: 
                     1   -     Φ   ⁡     (   x   )         =       ∏     y   =   1            L   ⁡     (   x   )              ⁢     (     1   -       Φ   ⁡     (     L   ⁡     (     x   ,   y     )       )       .                   (   1   )               
Calculations in accordance with Equation (1) are repeated for each path x for each source-destination pair.
 
     It is noted that a link in a path having a relatively low reliability will adversely affect the entire path performance, even if the remaining links have relatively high reliabilities. Therefore, it is advantageous to provide links with a small variance in reliability within a path. In certain preferred embodiments, this is accomplished by ensuring that:
 
Φ( L ( x,y ))≦α for all  y   (2).
 
Paths x that include links y that do not meet Equation (2) are eliminated from consideration.
 
     It is well known that the simultaneous transmission of a frame over two independent paths connecting a source and destination creates a higher reliability than if the frame were only transmitted via a single path. Applied to the present invention, when combining two independent paths, namely x 1  and x 2 , the effective reliability is expressed as:
 
1−Φ( x   1   ,x   2 )=1−Φ( x   1 )*Φ( x   2 )  (3),
 
and for N P  independent paths, the effective reliability of the combined N P  paths, denoted by 1−Φ(x 1 , x 2 , . . . , x N     p   ), is given by:
 
     
       
         
           
             
               
                 
                   
                     1 
                     - 
                     
                       Φ 
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             1 
                           
                           , 
                           
                             x 
                             2 
                           
                           , 
                           … 
                           ⁢ 
                           
                               
                           
                           , 
                           
                             x 
                             
                               N 
                               p 
                             
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         ∏ 
                         
                           w 
                           = 
                           1 
                         
                         
                           N 
                           p 
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             Φ 
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 w 
                               
                               ) 
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In certain embodiments, in addition to calculating the reliability of each of the possible paths, or effective reliability of groups of paths, at step  162 , sub-module  160  or another sub-module (not shown) performs an optional step  163  (shown by dashed lines) in which the throughput, number of hops, delay (tier and/or end-to-end), or a combination of one or more of throughput, number of hops and delay, for each of the possible paths is determined or calculated. This determination or calculation can be used in path selection to assign one or more paths that meet multiple constraints. 
     In additional embodiments, sub-module  160 , and in particular step  162  and optionally step  163 , considers statistics from the wireless process control and/or automation network, indicated by step  164  in dashed lines. Step  162  can determine reliability of each of the possible paths based on frame error rate statistics determined at each link, node and/or path. In addition, step  163  can obtain statistics at step  164  related to one or more of determined reliability, calculated throughput, calculated end-to-end delay and calculated tier delay. 
     A reliable path identification sub-module  170 , at step  172  identifies and selects a path, i.e., reliable paths 1−Φ(x), or set of paths, i.e., 1−Φ(x 1 , x 2 ) or 1−Φ(x 1 , x 2 , . . . , x N     p   ), from the possible paths x between a selected source-destination pair. The selected path or set of paths is identified by comparison to the minimum reliability requirements 1−Φ(i) specified in the set of routing rules  120 . Accordingly, paths meeting the following conditions are identified as reliable:
 
1−Φ( x )≧1−Φ( i )for each usage class  (5), and
 
| L ( x )| is smallest  (6).
 
Note that in circumstances in which combined independent paths are selected, i.e., a selected group of paths, the comparison of Equation (5) is carried out substituting 1−Φ(x 1 , x 2 ) calculated from Equation (3) or 1−Φ(x 1 , x 2 , . . . , x N     p   ) calculated from Equation (4) for 1−Φ(x).
 
     In certain embodiments, the paths and/or group of paths can be selected based on the condition that |L(x)| satisfies the following constraint:
 
| L   i   opt   |≧|L ( x )|  (7).
 
     Finally, a path assignment sub-module  180  assigns at step  182  the minimum number of reliable paths for the selected source-destination pair based on the minimum number of paths N i   opt  for a source-destination pair specified in the set of routing rules  120 . These paths can be then assigned in a path routing table  190 , where the notations “A,” “B,” “C” and “D” refer to different paths that meet the conditions of Equation (5) and have the lowest |L(x)|. Where the number of paths having the lowest |L(x)| value do not meet the minimum number of paths N i   opt  for a source-destination pair, the path(s) having the next largest |L(x)| are assigned so that the minimum number of paths N i   opt  for a source-destination pair is provided. In the alternative, the paths selected satisfy the conditions of Equation (7). As described further herein, in optional embodiments of the present invention, at step  182 , the path assignment sub-module  180  also considers additional constraints in assigning paths to the path routing table  190 , including throughput, delay (end-to-end and/or tier), number of hops, or a combination of one or more of throughput, number of hops and delay, as indicated by step  183  in dashed lines. 
     Furthermore, in additional embodiments of the present invention, the path assignment step  182  is iterative, wherein, based upon network statistics related to one or more of calculated reliability, number of hops, calculated throughput, calculated end-to-end delay and calculated tier delay, certain paths are discarded and replaced with additional paths to meet the minimum number of paths N i   opt  for a source-destination pair. This optional embodiment allows the system and method to be adaptive to continuously maintain optimal network traffic flow, and is comprehended in  FIG. 6  with a dashed connector between steps  162  and  182 . 
     In certain embodiments, several combinations of paths or groups of paths will meet the requirements of Equations (5)-(6). In these cases, the selection of the paths should seek a uniform distribution of traffic over the network. The method of the present invention therefore assigns the minimum number of paths N i   opt  for a source-destination pair and in certain embodiments additional alternate paths. For instance, as shown in path routing table  190 , up to two alternate paths are provided. The remaining set of paths N p −(N i   opt +2) are discarded. 
     For a particular source-destination pair, during normal operating conditions, data traffic is routed through the assigned paths rather than the alternate paths. However, if degradation in the usage class performance is sensed at either end, or at one of the links or nodes in an assigned path, data traffic passes through both the assigned paths and the alternate paths. 
     In certain alternative embodiments of the present invention, the minimum number of paths N i   opt  for a source-destination pair is dynamically adjusted based on the usage class reliability requirements 1−Φ c (i) and variations in network and/or traffic loading. The minimum number of paths N i   opt  that meet the network reliability requirements can be determined such that:
 
Φ( N   i   opt )≦Φ c ( i ), for all  i   (8).
 
     In an additional embodiment of the present invention, consideration is given to a maximum allowable delay in assignment of particular paths for a source-destination pair. Accordingly, if the calculated delay exceeds the maximum allowable delay for a given path, another path, e.g., a set of WED, WID, and/or WGD, can be added to minimize delay. Alternatively, or in conjunction, another radio frequency channel and/or hopping pattern can be employed to minimize delay for the given path. 
     In certain embodiments in which the path assignment is based on usage class, one or more paths x are assigned such that the following conditions are satisfied:
 
ψ( j,i,x )≦ψ( j,i ,max)for all  j,i , and  x   (9a), and
 
ψ( i,x )≦ψ( i ,max)for all  i  and  x   (9b).
 
Paths x that do not meet the conditions of Equation (9a) or Equation (9b) are discarded in this embodiment.
 
     In certain embodiments of the present invention, the maximum allowable delay is considered in selecting the minimum number of paths N i   opt  for a source-destination pair based on satisfaction of Equations (9a) and (9b). 
     In further embodiments of the present invention, the method and system of the present invention defines a maximum allowable delay for frame transmission within each tier j, ψ(i, j, max), as a function of the class i. The sum of all values ψ(i, j, max) for all j should not exceed the maximum system delay constraints. Because wireless process control and/or automation networks can be sensitive to delay, maintaining the transport delay at each tier within the system maximum allowable delay is desirable to ensure proper operation. 
       FIG. 7  is a schematic block diagram of a wireless process control and/or automation network routing system  200  according to another embodiment of the present invention. In general, the wireless process control and/or automation network routing system  200  includes an end-to-end delay minimization module  210 , a set of maximum allowable end-to-end delay rules  220 , e.g., in the form of a maximum allowable end-to-end delay table, and hardware  80  for executing the delay minimization module  210 . In general, the delay minimization module  210  is executable by suitably interconnected hardware  80 , such as one or more wireless gateway devices  80   a , a separate computing device  80   b , a combination of one or more wireless gateway devices  80   a  and a separate computing device  80   b , or other known processing device. The end-to-end delay minimization module  210  generally includes a path determination sub-module  150 , an end-to-end delay calculation sub-module  260 , a path identification sub-module  270  and a path assignment sub-module  280 . 
     Still referring to  FIG. 7 , and also referring to  FIG. 8 , the operation of an embodiment of the end-to-end delay minimization module  210  is shown in more detail. A path determination sub-module  150  determines at step  152  possible paths between a selected source-destination pair. This step  152  and module  150  operate, for instance, in the same manner as described above with respect to  FIGS. 5 and 6 . 
     Next, the end-to-end delay calculation sub-module  260  calculates at step  262  the end-to-end delay for each of the possible paths determined in step  152 . These calculations can be based upon network statistics incorporated at step  264 . For instance, each transmitted frame includes a timestamp with the time at which frame processing commences at the source. When the frame is received by the destination, a receipt timestamp is incorporated, and the end-to-end delay can be calculated based on the difference between the receipt time of the destination and the time that frame processing commenced at the source. This calculation accounts for all frame or packet processing time and transmission time at each node in the path. 
     In certain embodiments, in addition to calculating the end-to-end delay of each of the possible paths at step  262 , sub-module  260  or another sub-module (not shown) performs an optional step  263  (shown by dashed lines) in which the reliability, throughput, number of hops, tier delay, or a combination of one or more of reliability, throughput, number of hops and tier delay, for each of the possible paths is determined or calculated. This determination or calculation can be used in path selection to assign one or more paths that meet multiple constraints. 
     Next, at step  272 , the path identification sub-module  270  identifies acceptable paths by comparison of the calculated end-to-end delay with the maximum allowable end-to-end delay specified in the set of maximum allowable end-to-end delay rules  220 . The set of maximum allowable end-to-end delay rules  220  includes, in certain embodiments, specified maximum allowable end-to-end delay  224  per usage class  222 , denoted as ψ(i, max). Paths are identified as acceptable if Equation (9b) set forth above is satisfied. 
     Finally, a path assignment sub-module  280  assigns at step  282  the acceptable paths, i.e., paths that satisfy Equation (9b), to the routing table  190 . In additional embodiments of the present invention, at step  282 , the path assignment sub-module  280  also considers additional constraints in assigning paths to the path routing table  190 , including minimum reliability (e.g., following the module  110  described with respect to  FIGS. 5 and 6 ), maximum throughput, a maximum allowable tier delay, maximum number of hops, or a combination of one or more of minimum reliability, maximum throughput, maximum number of hops and minimum allowable tier delay, as indicated by step  283  in dashed lines. 
     During network transmission incorporating the system and method of the present invention, if a frame is received at the destination with a calculated end-to-end delay that exceeds the maximum allowable end-to-end delay, the path through which that frame passed will be identified in the network statistics as unacceptable for failing to satisfy the end-to-end delay constraint. This information will be used to dynamically discard that failed path from the routing table  190 , and replace that path with one or more additional paths, for instance, if necessary to meet any other specified constraints. 
     In addition, in still further embodiments of the present invention, the path assignment step  282  is iterative, wherein, based upon network statistics related to one or more of calculated reliability, calculated throughput, number of hops and calculated tier delay, certain paths are discarded and replaced with additional paths. The iterative nature of the end-to-end delay minimization module  210  allows the system and method to be adaptive to continuously maintain optimal network traffic flow, and is comprehended in  FIG. 8  with a dashed connector between steps  262  and  282 . 
       FIG. 9  is a schematic block diagram of a wireless process control and/or automation network routing system  300  according to yet another embodiment of the present invention. In general, the wireless process control and/or automation network routing system  300  includes a tier delay minimization module  310 , a set of maximum allowable tier delay rules  320 , e.g., in the form of a maximum allowable tier delay table, and hardware  80  for executing the delay minimization module  310 . In general, the delay minimization module  310  is executable by suitably interconnected hardware  80 , such as one or more wireless gateway devices  80   a , a separate computing device  80   b , a combination of one or more wireless gateway devices  80   a  and a separate computing device  80   b , or other known processing device. The tier delay minimization module  310  generally includes a path determination sub-module  150 , a tier delay calculation sub-module  360 , a link identification sub-module  370  and a path assignment sub-module  380 . 
     Still referring to  FIG. 9 , and also referring to  FIG. 10 , the operation of an embodiment of the tier delay minimization module  310  is shown in more detail. A path determination sub-module  150  determines at step  152  possible paths between a selected source-destination pair. This step  152  and module  150  operate, for instance, in the same manner as described above with respect to  FIGS. 5 and 6 . 
     Next, the tier delay calculation sub-module  360  calculates at step  362  the tier delay for each of the links or set of links in tier j for the possible paths determined in step  152 . These calculations can be based upon network statistics incorporated at step  364 . For instance, each transmitted frame includes a timestamp with the time at which frame processing commences at the source. When the frame is transmitted from the last node in the given tier, a transmission timestamp is incorporated, and the tier delay can be calculated based on the difference between the transmission time at the last node in the tier j and the time that frame processing commenced at the first node in the tier j. This calculation accounts for all frame or packet processing time and transmission time at each node in the path in tier j. 
     In certain embodiments, in addition to calculating the tier delay of each of the possible paths at step  362 , sub-module  360  or another sub-module (not shown) performs an optional step  363  (shown by dashed lines) in which the reliability, throughput, number of hops, end-to-end delay, or a combination of one or more of reliability, throughput, number of hops and end-to-end delay, for each of the possible paths is determined or calculated. This determination or calculation can be used in path selection to assign one or more paths that meet multiple constraints. 
     Next, at step  372 , the link identification sub-module  370  identifies acceptable links or sets of links by comparison of the calculated tier delay with the maximum allowable tier delay specified in the set of maximum allowable tier delay rules  320 . The set of maximum allowable tier delay rules  320  includes, in certain embodiments, specified maximum allowable tier delay  326  per usage class i  322  per tier j  328 , denoted as ψ(j, i, max). A link or a set of links is identified as acceptable if Equation (9a) set forth above is satisfied. The steps  362  and  372  are repeated for each tier j within a path, or unless a calculated tier delay exceeds the maximum allowable tier delay, at which point the path is discarded. 
     Finally, after Equation (9a) is satisfied for all tiers within a given path, the path assignment sub-module  380  assigns at step  382  the acceptable paths to the routing table  190 . In additional embodiments of the present invention, at step  382 , the path assignment sub-module  380  also considers additional constraints in assigning paths to the path routing table  190 , including reliability (e.g., following the module  110  described with respect to  FIGS. 5 and 6 ), throughput, a maximum allowable end-to-end delay, number of hops, or a combination of one or more of throughput, number of hops and tier delay, as indicated by step  383  in dashed lines. 
     During network transmission incorporating the system and method of the present invention, if a frame is received at the end of a tier with a calculated tier delay that exceeds the maximum allowable tier delay, that frame will be dropped, and the link or set of links within the tier will be identified in the network statistics as unacceptable as failing to satisfy the end-to-end delay constraint. This information will be used to dynamically discard the one or more paths including that link or set of links from the routing table  190 , and replace the one or more discarded paths with one or more additional paths, for instance, if necessary to meet any other specified constraints. 
     In addition, in still further embodiments of the present invention, the path assignment step  382  is iterative, wherein, based upon network statistics related to one or more of calculated reliability, calculated throughput, number of hops and calculated tier delay, certain paths are discarded and replaced with additional paths. The iterative nature of the tier delay module  310  allows the system and method to be adaptive to continuously maintain optimal network traffic flow, and is comprehended in  FIG. 10  with a dashed connector between steps  362  and  382 . 
       FIG. 11  is a schematic block diagram of a wireless process control and/or automation network routing system  400  according to still another embodiment of the present invention. In general, the wireless process control and/or automation network routing system  400  includes a delay minimization module  410 , a set of maximum allowable delay rules  420 , e.g., in the form of a maximum allowable delay table incorporating maximum allowable tier delay values  426  for tiers j  428  in a given usage class i  422  and maximum allowable end-to-end delay values  424  for a given usage class i  422 , and hardware  80  for executing the delay minimization module  410 . In general, the delay minimization module  410  is executable by suitably interconnected hardware  80 , such as one or more wireless gateway devices  80   a , a separate computing device  80   b , a combination of one or more wireless gateway devices  80   a  and a separate computing device  80   b , or other known processing device. The tier delay minimization module  410  generally includes a path determination sub-module  150 , an end-to-end delay calculation sub-module  460 , a potentially acceptable path identification sub-module  465 , a tier delay calculation sub-module  470 , a link identification sub-module  475  and a path assignment sub-module  480 . 
     Still referring to  FIG. 11 , and also referring to  FIG. 12 , the operation of an embodiment of the delay minimization module  410  is shown in more detail. While the steps of incorporating network statistics, and determining and employing the additional factors including reliability, throughput and total number of hops for the assignment of paths, are not specifically shown with respect to  FIG. 12  for sake of clarity, one of skill in the art will appreciate based on the previous embodiments described herein that these additional steps can be incorporated in the module  410 . 
     As shown in  FIG. 12 , a path determination sub-module  150  determines at step  152  possible paths between a selected source-destination pair. This step  152  and module  150  operate, for instance, in the same manner as described above with respect to  FIGS. 5 and 6 . 
     Next, the end-to-end delay calculation sub-module  460  calculates at step  462  the end-to-end delay for each of the possible paths determined in step  152 . These calculations can be based upon network statistics (not shown in  FIG. 12 ), for instance, as discussed with respect to  FIG. 8  (reference numeral  264 ). For instance, each transmitted frame includes a timestamp with the time at which frame processing commences at the source. When the frame is received by the destination, a receipt timestamp is incorporated, and the end-to-end delay can be calculated. This calculation accounts for all frame or packet processing time and transmission time at each node in the path. 
     In certain embodiments, for instance, as depicted in  FIG. 8  (reference numeral  263 ), in addition to calculating the end-to-end delay of each of the possible paths at step  462 , sub-module  460  or another sub-module performs an optional step in which the reliability, throughput, number of hops, or a combination of one or more of reliability, throughput and number of hops for each of the possible paths is determined or calculated. This determination or calculation can be used in identification of potentially acceptable paths as described below with respect to sub-module  465  and step  467  to designate one or more paths that meet multiple constraints. 
     Next, at step  467 , the potentially acceptable path identification sub-module  465  identifies potentially acceptable paths by comparison of the calculated end-to-end delay determined at step  462  with the maximum allowable end-to-end delay specified in the set of delay rules  420  (column  424 ). The set of delay rules  420  includes, in certain embodiments, specified maximum allowable end-to-end delay  424  per usage class  422 , denoted as ψ(i, max). Paths are identified as potentially acceptable if Equation (9b) set forth above is satisfied. 
     In the method of the module  410 , even though certain paths can be identified as potentially acceptable at step  467 , these potentially acceptable paths will not be assigned to the routing table  190  if any one of the tier delays exceeds the maximum allowable tier delay ψ(j, i, max). Therefore, the tier delay calculation sub-module  470  and link identification sub-module  475  are incorporated to ensure that the delay at each tier meets the constraints. In particular, the tier delay calculation sub-module  470  calculates at step  472  the tier delay for each of the links or set of links in tier j for the possible paths determined in step  152 . These calculations can be based upon network statistics, for instance, as described with respect to  FIG. 10  (reference numeral  364 ). For example, each transmitted frame includes a timestamp with the time at which frame processing commences at the source; when the frame is transmitted from the last node in the given tier, a transmission timestamp is incorporated, and the tier delay can be calculated based on all frame or packet processing time and transmission time at each node in the path in tier j. 
     In certain embodiments, in addition to calculating the tier delay of each of the possible paths at step  472 , sub-module  470  or another sub-module performs an optional step in which the reliability, throughput, number of hops, or a combination of one or more of reliability, throughput and number of hops for each of the possible paths is determined or calculated, as described with respect to  FIG. 10  (reference numeral  363 ). 
     Next, at step  477 , the link identification sub-module  475  identifies acceptable links or sets of links by comparison of the calculated tier delay with the maximum allowable tier delay specified in the set of maximum allowable tier delay rules  420 . A link or a set of links is identified as acceptable if Equation (9a) set forth above is satisfied. The steps  472  and  477  are repeated for each tier j within a path, or unless a calculated tier delay exceeds the maximum allowable tier delay, at which point the path is discarded. 
     Finally, after Equation (9a) is satisfied for all tiers within a given path, the path assignment sub-module  480  assigns at step  482  the acceptable paths to the routing table  190 . In additional embodiments of the present invention, at step  482 , the path assignment sub-module  480  also considers additional constraints in assigning paths to the path routing table  190 , including reliability (e.g., following the module  110  described with respect to  FIGS. 5 and 6 ), throughput, number of hops, or a combination of one or more of reliability, throughput and number of hops, as indicated by step  383  in  FIG. 10 . 
     In addition, in still further embodiments of the present invention, the path assignment step  482  is iterative, wherein, based upon network statistics related to one or more of determined reliability, calculated throughput, number of hops and calculated tier delay, certain paths are discarded and replaced with additional paths. The iterative nature of the delay module  410  allows the system and method to be adaptive to continuously maintain optimal network traffic flow, and is comprehended in  FIG. 12  with a dashed connector between steps  462  and  482 . 
     In additional embodiments as discussed above, the maximum allowable throughput for a given link η(L(x, y), max) is considered in the selection of the minimum number of independent paths N i   opt  and/or the assignment of particular paths for a source-destination pair such that the following condition is satisfied:
 
η( L ( x,y ))≦η( L ( x,y ),max)for all  y   (10).
 
     In the event that the minimum number of independent paths N i   opt  or the combination of the minimum number of independent paths N i   opt  and the allowed number of alternative paths cannot be assigned, one or more of the following can be implemented until the constraints are met: (1) add another path, e.g., a set of WED, WID, and/or WGD, to boost reliability, throughput or minimize delay; (2) improve the reliability of the weakest link through redundancy; and/or (3) use other RF channels and/or hopping patterns. 
     In still further embodiments of the present invention, based on the traffic distribution and throughput, the number of channels per selected paths is determined to ensure that the maximum allowable tier delay ψ(i, j, max) and η(L(x, y), max) are both satisfied. Paths with ψ(i, j, x) that exceed the maximum allowable tier delay ψ(i, j, max) or the end-to-end ψ(i, max) will either (1) be replaced with other paths, or (2) amended with multiple channels per path, in order to meet process control system usage class requirements. 
     In accordance with conventional data frame architecture that is well known to those skilled in the art, each frame is supplied with a digit indicating whether it is an original transmission or a retransmitted frame. In accordance with certain embodiments of the present invention, the conventional data frame architecture is modified to reflecting its usage class level. A usage class digit (UCD) is added in the routing table for each source-destination pair to be utilized during the routing of a frame. This UCD is utilized in data frame transmission so that frames are dropped if the frame usage class is greater than the UCD. That is, the system will route a frame only when the frame usage class is less than or equal to the UCD. In certain embodiments, for retransmitted frames, the process will allow passing the retried frames through the assigned and alternate paths irrespective of the UCD. 
     Table 3 below is a partial representation of a routing table between certain pairs of WIDs and WGDs that includes an indication of a UCD for the depicted pairs. Note that the pairs can be direct links or links with intermediate hops. For example, path 1 is a path between source address 4E22 and destination address 22A4, and is an assigned path for frames with a UCD of 3, whereby an initially transmitted frame with usage class 0, 1, 2 or 3 will be passed, but an initially transmitted frame with a usage class of 4 or 5 will not be passed. Path 2 is an alternative path between the same source-destination pair with a UCD of 5 or lower, whereby retransmitted frames of all classes will be passed through the path. Path 3 is an alternate path between the 4B78 and 22A4 source-destination address pair for all usage classes, i.e., all retransmitted frames will pass. Path 4 is an assigned path between 4E22 and 22D9 for all usage classes. Path 5 is an alternate path between 4EAA and 22D9 for class 0, 1 and 2 only. 
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 (Part of the) Routing table 
               
             
          
           
               
                   
                 Source 
                 Dest. 
                   
                   
               
               
                   
                 Address 
                 Address 
               
               
                 Path 
                 WID 
                 WGD 
                 UCD 
                 Path Type 
               
               
                   
               
               
                 1 
                 4E22 
                 22A4 
                 3 
                 AS 
               
               
                 2 
                 4E22 
                 22A4 
                 5 
                 AL 
               
               
                 3 
                 4B78 
                 22A4 
                 5 
                 AL 
               
               
                 4 
                 4E22 
                 22D9 
                 5 
                 AS 
               
               
                 5 
                 4EAA 
                 22D9 
                 2 
                 AL 
               
               
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
               
               
                 AS = Assigned Path 
               
               
                 AL = Alternate Path 
               
             
          
         
       
     
     The method and system of the present invention includes dynamic adjustment of routing to allow assigned and alternative paths to pass traffic irrespective of the usage class when either of the following events occur: (a) when a timeout occurs, either due to a violation of the maximum allowable delay (tier and/or end-to-end) or because an acknowledge message is not received, the assigned and alternate paths for the source-destination pair (where the timeout occurs) will allow all frames to pass irrespective of the usage class; (b) when the frame error probability for a link within an assigned path exceeds a specified threshold, all source-destination pairs with an assigned path through this link allows the assigned and alternate paths to pass all traffic. A message for adjustment of the routing table  190  for WGDs and WIDs can be initiated by the master WGD and/or the device that executed the route optimization module  110 . The adjustment of the routing table can be effective for a preset time duration, or until a second message is received requesting reversion to normal routing settings. 
     In additional embodiments of the present invention, a combination of the above-described constraints is implemented to optimize and select routes for a wireless process control and/or automation network. For each particular pair of source and destination, N, is minimized such that Equation (8) is satisfied for all i, with the additional conditions that Equations (2), (6), (9a) and (10) are satisfied. If any of Equations (8), (2), (6), (9a) and (10) are not satisfied, than: 
     a. another path, i.e., a set of WED, WID and WGD, can be added to boost reliability, throughput or minimize delay; 
     b. the reliability of the weakest link can be improved through redundancy; 
     c. other radio frequency channels and/or hopping patterns can be used; or 
     d. any combination of (a), (b) and (c) can be implemented. 
     The process is repeated for each source-destination pair in the wireless process control and/or automation network, or each source-destination pair in the wireless process control and/or automation network for which optimization according to the present invention is desired. 
     The above route optimization module described with respect to  FIGS. 5 and 6 , optionally including the additional steps or sub-modules, can be implemented with respect to the entire network or certain source-destination pairs. In embodiments in which the path optimization process is implemented for the entire network, the above process, optionally including the additional steps or embodiments, is repeated for each source-destination pair in the system. In embodiments in which the path optimization process is implemented for certain selected source-destination pairs, the above process, optionally including the additional steps or embodiments, is repeated for the source-destination pairs to be optimized. To prevent channel congestion with respect to pairs that are not optimized, routing rules can be implemented that prioritize the selected source-destination pairs through the assigned paths, or through the assigned paths and alternate paths in embodiments in which alternate paths are provided. In further embodiments, the assigned paths, or the assigned paths and alternate paths in embodiments in which alternate paths are provided, can be reserved exclusively for the source-destination pairs selected for optimization according to the method and system of the present invention. 
     Illustrative Example 
     For the purpose of demonstrating a wireless process control system using the optimization process and system of the present invention, reference is made to the portion of an ISA-SP100 network shown in  FIG. 13 . The portion depicted includes a single source-destination pair with multiple paths. Each wireless link has a maximum capacity of 250 kbps, and an effective achievable throughput of 100 kbps, since the maximum achievable throughput is typically in the range of 40% of link capacity for CSMA-CA protocols and the like. The links&#39; frame error rate profiles are given in Table 4, which also provides the existing levels of throughput per link. The process control equipment at WID L 13  is assumed to generate 60 kbps when commissioned to the network, where 40 kbps is the traffic going to the CCR (uplink) and 20 kbps is the traffic coming from the CCR to L 13  (downlink). 
     Frame retransmission rates are assumed to be below 1% for all classes of service. It should be noted that these FER values will depend on the specifics of the underlying physical layer, e.g., type of digital modulation and error control coding, radio channel path loss and fading, co-channel interference, etc. For illustration, typical FER values are assumed. 
     In Table 5, the required FERs per class are listed, and a typical traffic mix across the different classes of service is represented by the percentage of frames belonging to Class 0, 1, 2, 3, 4 and 5. In addition, assumed limits for total end-to-end delay and per-tier delay are specified. In general, delay values will be related to the traffic loading and queuing/priority mechanisms. Actual delay values per link can be obtained empirically from message timestamps. Depending on the number of hops that a given frame has to make, the accrued delay can be computed, which are accounted for in the optimization system and method of the present invention to provide a certain end-to-end delay. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                   
                   
                   
                 η(L(x, y)) 
               
               
                   
                 Source 
                 Destination 
                 Link FER 
                 (kbps) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 L13 
                 L23 
                 1.00E−05 
                 0 
               
               
                   
                 L13 
                 L24 
                 1.00E−06 
                 0 
               
               
                   
                 L13 
                 L25 
                 5.00E−07 
                 0 
               
               
                   
                 L13 
                 L26 
                 1.00E−07 
                 0 
               
               
                   
                 L23 
                 L32 
                 5.00E−04 
                 60 
               
               
                   
                 L24 
                 L32 
                 5.00E−06 
                 30 
               
               
                   
                 L25 
                 L32 
                 5.00E−04 
                 70 
               
               
                   
                 L26 
                 L32 
                 5.00E−03 
                 90 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                   
                 Maximum 
                   
                 End-to- 
                   
                   
                   
               
               
                   
                 Allowable 
                 Traffic 
                 End 
                 Tier 1 
                 Tier 2 
                 Tier 3 
               
               
                   
                 FER 
                 Mix 
                 ψ 
                 ψ 
                 ψ 
                 ψ 
               
               
                 Class 
                 Φ c  (i) 
                 D i   
                 (i, max) 
                 (i, 1, max) 
                 (i, 2, max) 
                 (i, 3, max) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 1.00E−08 
                 0% 
                 0.3 sec 
                 0.1 sec 
                 0.1 sec 
                 0.1 sec 
               
               
                 1 
                 1.00E−08 
                 8% 
                 0.5 sec 
                 0.2 sec 
                 0.2 sec 
                 0.1 sec 
               
               
                 2 
                 1.00E−07 
                 10% 
                 0.5 sec 
                 0.2 sec 
                 0.2 sec 
                 0.1 sec 
               
               
                 3 
                 1.00E−06 
                 12% 
                   1 sec 
                 0.4 sec 
                 0.3 sec 
                 0.3 sec 
               
               
                 4 
                 1.00E−05 
                 35% 
                   5 sec 
                   2 sec 
                   2 sec 
                   1 sec 
               
               
                 5 
                 1.00E−05 
                 35% 
                   5 sec 
                   2 sec 
                   2 sec 
                   1 sec 
               
               
                   
               
             
          
         
       
     
     Applying the given data into the process simulation model, the paths&#39; frame error probabilities are calculated as shown in Table 6. The frame error probabilities when transmitting frames over multiple independent paths are then calculated as in Table 7. Based on the optimized routing method and system of the present invention, the assigned and alternating paths are given in Table 8. For the purpose of the present example, no more than 2 paths are assigned. 
     Table 9 provides the resulting links&#39; throughputs following the path assignment of Table 8. Since the throughput of L 26 -L 32  exceeds 100 kbps, a second RF channel is provided to support this traffic. 
     
       
         
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                   
                 Path 
                   
               
               
                 Path 
                 Designation 
                 Φ(L(x, y)) 
               
               
                   
               
             
             
               
                 L13-L23-L32 
                 A 
                 5.10E−04 
               
               
                 L13-L24-L32 
                 B 
                 6.00E−06 
               
               
                 L13-L25-L32 
                 C 
                 5.00E−04 
               
               
                 L13-L26-L32 
                 D 
                 5.00E−03 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Associated FER with Selected Paths 
               
             
          
           
               
                   
                 x 
                 Φ(x) 
                 x 
                 Φ(x) 
               
               
                   
                   
               
               
                   
                 A 
                 5.10E−04 
                 B &amp; C 
                 3.00E−09 
               
               
                   
                 B 
                 6.00E−06 
                 B &amp; D 
                 3.00E−08 
               
               
                   
                 C 
                 5.00E−04 
                 C &amp; D 
                 2.50E−06 
               
               
                   
                 D 
                 5.00E−03 
                 A &amp; B &amp; C 
                 1.53E−12 
               
               
                   
                 A &amp; B 
                 3.06E−09 
                 A &amp; B &amp; D 
                 1.53E−11 
               
               
                   
                 A &amp; C 
                 2.55E−07 
                 B &amp; C &amp; D 
                 1.50E−11 
               
               
                   
                 A &amp; D 
                 2.55E−06 
                 A &amp; B &amp; C &amp; D 
                 7.66E−15 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                   
                 Assigned 
                 Alternate 
               
               
                 Class 
                 path 
                 path 
               
               
                   
               
             
             
               
                 0 
                 A &amp; B 
                 C &amp; D 
               
               
                 1 
                 A &amp; B 
                 C &amp; D 
               
               
                 2 
                 A &amp; B 
                 C &amp; D 
               
               
                 3 
                 A &amp; B 
                 C &amp; D 
               
               
                 4 
                 B 
                 A &amp; C 
               
               
                 5 
                 B 
                 A &amp; C 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 Link Throughput 
               
             
          
           
               
                   
                   
                 Throughput 
               
               
                 Source 
                 Destination 
                 (kbps) 
               
               
                   
               
             
          
           
               
                 L13 
                 L23 
                 46 
               
               
                 L13 
                 L24 
                 60 
               
               
                 L13 
                 L25 
                 40 
               
               
                 L13 
                 L25 
                 40 
               
               
                 L23 
                 L32 
                 92 
               
               
                 L24 
                 L32 
                 90 
               
               
                 L25 
                 L32 
                 90 
               
               
                 L26 
                 L32 
                 110 
               
               
                   
               
             
          
         
       
     
     The “normalized” spectrum usage (counted per RF channel use) can be estimated by taking into account the total number of RF channel occupancies for the end-to-end connection. This can be calculated as follows: 
                   U   =       ∑   i     ⁢       D   i     ⁢     N   i                 (   11   )               
where D i  represents the traffic distribution percentage for class i, and N i  is the number RF channels occupied per class. This expression applies to the standard (i.e., non-optimized) operation procedure. However, with the optimization algorithm of this invention, the normalized spectrum usage becomes:
 
                   U   =         ∑   i     ⁢       D   i     ⁢     N   i   opt         +       P   ret     ⁢       ∑   i     ⁢       D   i     ⁡     (       N   i   opt     +   2     )                     (   12   )               
where P ret  is the average retransmitted probability in the system. By applying these formulas for the specific parameters used in this example, under standard non-optimized operation the following result for spectrum utilization is attained:
 
 U= 1+4*(0%+8%+10%+12%+35%+35%)=5,
 
since there is one RF transmission from L 13  to a WID, and four separate RF transmissions going from WID to WGD. On the other hand, the normalized spectrum usage is obtained as follows for the case of the process optimization of this invention:
 
 U=[ 1+2*(8%+10%+12%)+1*(35%+35%)]+0.01*4 [(8%+10%+12%)+3*(35%+35%)]=2.4 where 1% retransmission probability is assumed.
 
     The ratio of 5/2.4≅2 indicates that double the spectrum would be required if the process optimization of this invention is not followed. Notably, these savings in spectrum consumption do not preclude meeting the minimum usage class requirements. 
     This optimization procedure can also significantly reduce power consumption for the nodes. Battery power usage is directly proportional to the number of transmitted and received frames, and is not significantly impacted by other processing activities such as encryption, authentication, heartbeat signal, and the like.  FIGS. 14 and 15  show the normalized power usage (which is proportional to the number of frames transmitted and received) from L 13  to L 32 , with and without the optimization scheme. Note that for the purpose of  FIGS. 8 and 9 , a single transmission consists of a frame sent from L 13  to L 32  and the acknowledgement frames sent from L 32  to L 13 . 
       FIG. 14  indicates that the number of received frames for the four WIDs remains the same with and without the optimization scheme, whereas the number of transmitted frames drops from 8 to 2.3 frames when the optimization scheme is implemented.  FIG. 15  reveals that the number of frames received by the WED and WGD drop from 8 to 2.6 for a single transmission, while the number of transmitted frames remain unchanged. Thus, the implementation of the optimization scheme extends battery lifecycle by 55% (16/10.3) for WIDs, and by 117% (10/4.6) for WEDs. 
     The method and system of the present invention have been described above and in the attached drawings; however, modifications will be apparent to those of ordinary skill in the art and the scope of protection for the invention is to be defined by the claims that follow. In addition, while certain implementations of the present invention have been described with respect to the ISA-SP100 protocol, the present invention can also be implemented within other wireless process control and/or automation protocols including but not limited to the HART® protocol.