Patent Publication Number: US-7594006-B2

Title: Trending method and apparatus for resource demand in a computing utility

Description:
BACKGROUND OF THE INVENTION 
   The present invention relates to utility computing. In a utility computing environment, utilization is improved by increasing the availability of servers and other computing resources to more people and their applications. Instead of sitting idle for a single application, these resources are used to execute programs for many users. Information technology infrastructure costs are reduced as computer resources are not purchased to only solve a single complex task for a department or division in a company. Instead utility computing allows the computer resources to be used by many different people during both peak periods and periods otherwise considered off-peak. Properly implemented, utility computing reduces the need for more resources as existing resources can be shared. 
   Utilization efficiency in the utility computing facility depends to a large extent on governing access to the pools of resources associated with the utility computing facility. It also depends on the ability of the system to accommodate the application demand and usage requirements in the future. Unfortunately, existing conventional systems have not been able to properly monitor or anticipate access to these pools of resources and deal with the relatively complex demand patterns that may be present in an enterprise or organization. 
   A number of conventional solutions only assure users and applications that a “best effort” will be made to allocate certain computing resources. The best effort approach does not allow for higher assurances if the customers are interested in higher availability of resources. 
   Other solutions allow customers to make monetary bids on computing utilities thereby indicating a desired quality of service or service assurance when using the resources. These systems are often driven by service level agreements or SLAs with higher paying customers receiving higher levels of service and resources. It remains unclear; however, what quality of service customers entering lower monetary bids are provided given the focus on this higher paying customer base. 
   Yet other utility computing solutions gauge access to pools of resources based upon transaction response times for different applications. The systems managing resources in this manner are complicated. They tie quality of service to the responsiveness of a particular application rather than the overall responsiveness of resources in the computing utility. This approach to resource management may improve performance for certain applications but overall may not improve the performance or efficiency associated with the computing utility. 
   As companies cut costs in information technology budgets, there is parallel demand to improve the information technology infrastructure for people to work more efficiently. Large server farms and clusters of computers can be used to improve the utilization of computing resources in an enterprise or company if utility computing is deployed effectively. Indeed, for certain applications having predictable execution schedules and demand requirements the conventional utility computing environments previously described are more useful. For example, conventional utility computing environments are more useful for batch programs as they are scheduled to run in advance and have certain predictable demand requirements during execution. 
   Unfortunately, implementing utility computing for business applications that are critical to the operation of a company is a much more difficult task. These business applications are generally very different in nature and have non-uniform computing needs. If a computing utility is unable to provide the necessary resources, business processes may not be performed resulting not only in delayed productivity but reduced business transactions and lost revenue. Improved controls for computing utility environments are needed to efficiently run business, engineering, and other applications having less predictable demand or schedules for demand yet require precise levels of assurances regarding access to resources. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram overview of a system for governing access to resources in a computing utility facility in accordance with one implementation of the present invention; 
       FIG. 2A  is a set of demand profile tables designed in accordance with one implementation of the present invention; 
       FIG. 2B  is a series of block diagrams illustrating a statistical framework for estimating the computing resources needed to satisfy joint application resource demands in accordance with the present invention; 
       FIG. 3  is a block diagram of a system used in one implementation for performing the apparatus or methods of the present invention; 
       FIG. 4  is a flowchart diagram providing the operations for governing access to resources in a computer utility facility in accordance with one implementation of the present invention; 
       FIG. 5  is a flowchart diagram of the operations that combine the multiple demand profiles and class of service requirements in accordance with one implementation of the present invention; 
       FIG. 6  is a schematic diagram illustrating the one or more class of service used in accordance with one implementations of the present invention; 
       FIG. 7  is a flowchart diagram of the operations used to police requests for resources from admitted applications in one implementation of the present invention; 
       FIG. 8  is a flowchart diagram further detailing one implementation of the present invention for policing of requests for resources by one or more applications; 
       FIG. 9  is a schematic diagram of various time periods and sliding windows used to determine an entitlement value in accordance with implementations of the present invention; 
       FIG. 10  is flowchart diagram detailing the operations for arbitration of resources in accordance with one implementation of the present invention; 
       FIG. 11  is schematic diagram for updating a demand profile for an application as the application&#39;s resource demand exhibits a trend and changes over time; and 
       FIG. 12  is a flowchart diagram of the operations associated with updating a demand profile in accordance with one implementation of the present invention. 
   

   Like reference numbers and designations in the various drawings indicate like elements. 
   SUMMARY OF THE INVENTION 
   One aspect of the present invention features a method and system of updating a demand profile used in a computing utility. The updating operation includes receiving a demand profile associated with an application that identifies a required resource demand during time slots in a demand cycle, receiving trending specification information used during admission to the computing utility and updating the demand profile when indicated in light of trending specification information and resource demand. 
   DETAILED DESCRIPTION 
   Aspects of the present invention are advantageous in at least one or more of the following ways. Updating the demand profile over time incorporates trends or trending in the overall resource demand for an application. The user or customer submitting the application to a computing utility specifies an initial demand profile and trend prediction upon admission to the computing facility. Application of the trend prediction along with observed data allows the demand profile to be used over longer periods of time even though the demand profile for the application is not static and is changing over time. 
   In addition to extending the lifetime of the demand profile for an application, implementations of the present invention make it easier for customers using the computing facility. Trending allows the updates to the demand profiles to occur dynamically with little or no user intervention. This obviates the time consuming process of capacity planning for each application and allows the computing utility instead to incorporate the underlying tasks of collecting and analyzing data to predict future resource demands. It is also advantageous for the computing utility as it reduces the likelihood of underestimating the costs and amount of resources needed by an application admitted and running within the utility over a period of time. 
     FIG. 1  is a block diagram overview of a system for governing access to resources in a computing utility facility in accordance with one implementation of the present invention. System  100  includes a series of customers  102 ,  104  and  106  each having an application and an application demand profile with class of service designations. As previously mentioned, each demand profile is enhanced with information and functionality associated with the entitlement profile of the present invention. Alternate implementations of the present invention can readily be scaled to accommodate customers having multiple applications and corresponding multiple demand profiles. 
   In this particular implementation, customers  102 ,  104  and  106  in system  100  communicate over network  112  to a resource access management (RAM) framework  108 , a programmable computing utility  110  and resource pools  114 ,  116 , and  118 . Alternatively, customers  102 ,  104  and  106  can communicate directly to other portions of system  100  rather than over network  112 . Class of service designations correspond to each application and may be different even if the same customer operates multiple different applications on system  100 . 
   Resource pools  114 ,  116  and  118  include a range of resources including resource  122  to resource  124 , resource  126  to resource  128  and resource  130  to resource  132  respectively. Each range of resources may include one or more different resources arranged in different organizational schemes as appropriate for the particular customers/applications being served and as required logistically by the system setup. For example, resources can be pooled according to the type of resource (i.e., pools of storage devices, pools of processors, pools of graphics rendering processors or pools of network nodes), the quality of the resources, (i.e., pools of high-availability devices and pools of medium reliability devices or low-cost devices) or any other logical method of grouping the resources. Additional groupings of these resources may be implemented either logically or physically to better provide for the different classes of service as needed. 
   Customers  102 ,  104  and  106  submit application demand profiles along with their applications to resource access management framework  108 . The demand profile associated with each application describes the pattern of demand for certain resources in one or more pools of resources as a series of cycles or as a polycyclic representation of demand over time. In accordance with the present invention, customers also specify a class of service on a per application basis for the computing utility facility to consider when admitting the application. A single class of service for a particular application can be specified or the class of service may vary depending on the time and date. Accurately predicting overall demand for resources by the various applications depends on the accurate representation of resources needed in each of the demand profiles, the cyclic demand on these resources made by the applications and the class of service associated with each application. Both the quantity and quality of underlying trace data used to construct the demand profile affects the accuracy of predicting demand. 
   Resource access management framework  108  qualifies and admits certain applications in accordance with implementations of the present invention before the applications are able to make requests for resources and begin processing data, run business applications or otherwise utilize any of the resources associated with programmable computing utility  110 . In particular, computing utility  110  ensures that the class of service requested by an operator or application can be provided in light of the polycyclic constraint on resources from one or many different applications and customers. 
   Once admitted, resource access management framework  108  continues to police admitted applications to ensure they do not attempt to over utilize resources, impact other admitted applications or otherwise operate outside their submitted demand profiles. Class of service level designations associated with each application do not alter the policing operation yet influence how resources are subsequently distributed or reallocated to those applications flagged during this process. Overall, subsystems within computing utility  110  work together on behalf of the individual applications to ensure data processing and storage access continues once they have been admitted and entitled to the various actual resources. 
     FIG. 2A  is a set of demand profile tables designed in accordance with one implementation of the present invention. These example demand profiles tables include a demand profile A  202 , a demand profile B  204  and a caveat demand profile  206  for a resource in pool of resources “X”. Each table in this example contributes a different cycle of demand and time varying class of service forming a polycyclic demand for a resource by the application. While other resources may be used by the application they are omitted for brevity and clarity of this example. Accordingly, additional resources would be specified in different demand tables corresponding to other resources and pools of resources. Class of service may also be specified in different tables and associated with applications operating on different dates and times. 
   Alternate implementations can organize the demand profiles and tables of the present invention in many different ways including multi-dimensioned data structures and objects having a hierarchical organization using inheritancy and other object-oriented features. They also may include different notations and granularities for referencing schedules. For example, a 24-hour notation could be used specifying all hours of the day rather than the conventional time indicated to avoid ambiguities between A.M. and P.M. hours. In addition to example values illustrated in  FIG. 2A , alternate implementations may use scalar values, values representing distributions or values representing data that contributes to such distributions. Further the illustrated demand profiles separate weekdays form weekends however, alternate schemes for organizing calendar dates can also be adopted that organize dates according to days, weeks, months, years or any other divisions that satisfy the particular needs of the implementation. 
   As previously mentioned, the complete demand profile for an application is composed of many smaller individual cycles and form a polycyclic pattern of demand. In the present example in  FIG. 2A , demand profile A  202  represents the cycle of demand during weekdays by a particular application for a particular resource pool X. Each application also specifies a desired time varying class of service for processing the application at the various points in time as illustrated. 
   The demand in this example is divided into 1-hour time slots and assumed to be statistically identical throughout each 1-hour time slot. For example, demand profile A  202  indicates that the demand for a resource pool X by the application is higher in the morning (i.e., 8:00 am to 9:00 am) and the later afternoon (i.e., 2:00 pm to 3:00 pm) Monday through Thursday. 
   Each hour in demand profile A  202  also specifies a class of service associated with processing the particular application at the particular time slot or period. Depending on the implementation of the present invention, the class of service entered in demand profile A  202  may represent the minimum requested class of service desired and acceptable by the application. If the utility delivers a lower class of service to the application the utility may be penalized. Likewise; the utility can also deliver a class of service equal to or higher than the minimum class of service to avoid penalties. Depending on the actual service agreement, the utility may or may not receive a premium for delivering a class of service beyond the minimum entered in the demand profile. Details on the different class of service levels and their use in allocating resources are described in further detail later herein. 
   According to demand profile A  202 , the demand profile for this resource on a Friday is different from the demand profile for the same resource during the other days of the week. Similarly, the class of service designations in demand profile A  202  also varies from day to day and hour to hour. This time varying class of service specified with each application allows processing power and associated fees for processing the applications to be efficiently and dynamically distributed rather than constantly or statically distributed to the same application or applications over time. As illustrated, demand profile A  202  also reflects expected uncharacteristic spikes in demand that may arise as noted on Thursday at 11:00 am where the demand index rises to “93” rather than 15 or 16 as on preceding days. Tailoring the class of service required and demand levels in accordance with the present invention allows resources to be utilized more efficiently and at a lower price point to the end users. Of course, while 1-hour slots have been used to simplify this example, alternate implementations of the present invention may use different size time slots or variable time slots of any equal or unequal durations. 
   Demand profile B  204  is a different table representing the demand and class of service by the same application on weekends rather than during the week. Consequently, to determine the overall demand from the application, demand profile A  202  (weekday) is combined with demand profile  204  (weekend) forming the polycyclic demand with time varying class of service requirements for the resource. Alternate implementations could combine more than two different cycles to create more refined and complex polycyclic demand patterns. 
   An additional caveat demand profile  206  can also be added to the polycyclic demand to represent events that occur more infrequently or over longer periods of time. Despite the potential infrequency of these events occurring, implementations of the present invention also combine time varying class of service with these events. Events entered in caveat demand profile  206  may include special events, holidays, seasonal occurrences and even emergencies that happen to have an element of predictability. For example, caveat demand profile  206  in  FIG. 2A  has three entries for three potentially different caveat type events. In this example, events A, B, and C have a start date and an end date with an associated demand level for several hours during this time period. If the start date and end date cover only two days then the demand levels entered in caveat demand profile  206  are used on the start date and end date respectively. When more than two days are covered, the demand levels associated with the start date and end date are used to approximate a demand curve for the time period between the dates bounding the time interval. Class of service entries specified can also be treated in a similar manner. In some situations, class of service remains a constant value over the caveat period while other situations may deem it appropriate to approximate the class of service linearly or with a curve fitted to cover the particular caveat period. 
   Alternate implementations can organize caveat demand profile  206  in many other ways and may or may not use start and end dates as illustrated in  FIG. 2A . For example, events in a caveat demand profile can be specified according to a pattern of dates. This pattern could include specifying particular calendar dates such as, “the last two business days of the month” or “the first Thursday in November.” In any event, the time slots, demand values and class of service in caveat demand profile  206  are also combined with demand profile A  202  and demand profile B  204  to create a resulting overall polycyclic demand to represent demand for the various resources in the computing facility. Further, caveat demand profile  206  may even hold pointers to replacement demand profiles to be used from the specified start date to end date in lieu of actual profile data. 
     FIG. 2B  is a series of block diagrams illustrating a statistical framework for estimating the computing resources needed to satisfy joint application resource demands in accordance with the present invention. Each resource used by an application can be modeled as a demand for the resource during a time slot in a series of time slots over a period of time. While not illustrated explicitly, the demand and associated probabilities for these demands are derived from trace data gathered on the particular application and resources used over various intervals. For example, the hourly demand for a resource over a 24 hour period would be modeled using the historical demand for the resource during a 60-minute time slots t for T=24 or 24 hours. Given a large enough set of historical samples from the application, one can reasonably determine the subsequent probability that an application would require a maximum number of resources in each of the time slots over the time period being measured. 
   Historical data week  208  through historical data week  210  provide the data for constructing a probability mass function (PMF) from W weeks of data collected during a 9 a.m. to 10 a.m. time slot. In this example, historical data gathered from trace data taken each workday over W weeks for a total of 5W samples indicates that the application required a minimum of 1 server and a maximum of 5 servers during the time slot being considered. PMF table  212  summarizes this data collected over W weeks as a set of probabilities that the application would need the indicated number of servers with the same results indicated graphically using application bar chart  214 . Inherent uncertainty exists in using the PMF for predicting subsequent application resource demands upon the computer utility facility especially when the 5W or other sample sizes are small. Accordingly, the computing utility facility accounts for this inaccuracy by computing confidence intervals for each of the probabilities in PMF table  212 . 
   An overall utility profile is then obtained for the 9 a.m. to 10 a.m. time frame by performing a similar calculation for each of the applications admitted to using the computer utility facility. The combination of these calculations results in a PMF utility profile  216  to describe the overall resource requirement for servers in the utility. Accuracy of the resulting PMF utility profile  216  affects the computing utility facility&#39;s ability to accurately assess and admit different applications with their requests for resources. By increasing the number of observations in creating PMF utility profile  216 , the computing utility facility is able to narrow the confidence intervals and thereby increase the accuracy for predicting resource demands. Additional information on determining the resource demands for applications in a computing facility utility is described in the whitepaper, “Statistical Service Assurances for Applications in Utility Grid Environments”, by Jerry Rolia, Xiaoyun Zhu, Martin Arlitt, Artur Andrzejak, Internet Systems and Storage Laboratory, HP Laboratories, Palo Alto, HPL-2002-155 Jun. 13, 2002. 
     FIG. 3  is a block diagram of a system  300  used in one implementation for performing the apparatus or methods of the present invention. System  300  includes a memory  302  to hold executing programs (typically random access memory (RAM) or read-only memory (ROM) such as a flash ROM), a presentation device interface  304  capable of interfacing and driving a display or output device, a processor  306 , a program memory  308  for holding drivers or other frequently used programs, a network communication port  310  for data communication, a secondary storage  312  with a secondary storage controller and input/output (I/O) ports and controller  314  operatively coupled together over interconnect  316 . System  300  can be preprogrammed, in ROM, for example, using field-programmable gate array (FPGA) technology or it can be programmed (and reprogrammed) by loading a program from another source (for example, from a floppy disk, a CD-ROM, or another computer). Also, system  300  can be implemented using customized application specific integrated circuits (ASICs). 
   In one implementation, memory  302  includes a admission system component  320 , a calendaring component  322 , a pooling component  324 , a policing component  326 , an arbitration component  328 , an assignment component  330 , a class of service component  332 , a monitoring component  334 , a knowledge management component  336  and a run-time module  338  that manages system resources used when processing one or more of the above components on system  300 . 
   As illustrated, these various modules of the present invention appear in a single computer system. However, alternate implementations could also distribute these components in one or more different computers to accommodate for processing demand, scalability, high-availability and other design constraints. Similarly, components illustrated in  FIG. 3  that appear to be discrete and separate from each other could be combined to effectuate higher efficiencies, lower costs or any other design constraint needed to implement aspects of the present invention in a large-scale enterprise or small-scale operating environment. For example, calendaring component  322  and admission component  320  are illustrated as discrete components however it may be more advantageous to combine these components if doing so would increase performance and scalability of the overall system implementation. 
   Admission system component  320  is responsible for determining if a customer and a given application can be granted admission to use the computing utility facility based on a provided demand profile. Admission system component  320  analyzes both the typical cyclical portions of an application demand profile as well as the caveat driven portions of the demand cycle when making a determination whether to admit or not admit a particular application to the computing utility facility. Details on one implementation of these operations are described in further detail later herein. 
   Calendaring component  322  maintains one or more calendars used in determining available resources and admitting or not admitting additional applications to the computing utility facility. In one implementation, calendars include time slots corresponding to each hour of usage each day of the week for several years at a time. Alternatively, calendars can track seconds, minutes, weeks, months, or years depending on the granularity required and application requirements. Entries are made on a staging calendar until the application entries are admitted to the computing utility facility and then added to a permanent calendar upon admission. To compartmentalize this information, the staging calendar and permanent calendar can be logically different calendars or alternatively can be the same calendar with a status flag indicating that certain entries in the calendar are tentative or staged while other entries in the calendar are permanent entries. Alternate implementations can arrange tentative and permanent entries in calendaring component  322  in many other ways in addition to those described above. 
   Pooling component  324  is a component used to organize and present the various resources available to system  300  as one or more resource pools. The resources pooled together may include storage, computing resources, network bandwidth and any other resource being requested by customers running applications. As previously described, these resources can be pooled together based on the type of resource (i.e., pools of storage devices, pools of processors, pools of graphics rendering processors or pools of network nodes), the quality of the resources, (i.e., pools of high-availability devices and medium reliability devices or low-cost devices) or any other logical or physical method of grouping the resources. Alternatively, pools of resources can also be grouped together according to a class of service they are to provide. 
   Once an application is admitted, policing component  326  ensures subsequent requests for resources from the admitted applications are within an acceptable range according to the application&#39;s associated demand profile. Policing component  326  intercepts and rejects requests for resources made outside the acceptable range thus reducing the likelihood that certain resources will become overbooked and/or unavailable. As previously described, class of service does not change the policing function directly but instead affects the way resources are subsequently distributed to applications identified by policing component  326 . Further, policing component  326  also considers the entitlement profile and burstiness of an application when performing application level policing functions. Details on policing with respect to entitlements are described in further detail later herein. 
   Arbitration component  328  intervenes when more than one application is entitled to a limited resource associated with the computing utility facility. To resolve conflict between applications, arbitration component  328  may implement one or more different operations to resolve the contention for the limited resource. For example, arbitration component  328  considers class of service and service level agreements (SLA) to determine a arbitration result that minimizes fines to the computing operation facility. In general, arbitration may be necessary if admission component  320  admits an application that overbooks one or more resource pool. 
   Once a resource is granted, assignment component  330  performs the necessary tasks and operations to assign the resources from the computing utility facility to a particular application. Assignment component  330  can perform the assignments under one or more different policies. For example, assignment component  330  can assign a first available resource to an application; assign a resource to an application that minimizes the latency for using a particular resource or resources with the application; or assignment component  330  can prioritize the order of assignment according to an application&#39;s class of service. Alternatively, assignment component  330  may even defer to a separate assignment module that performs the assignment using a different or proprietary approach to assigning resources. 
   Class of Service component  332  processes the requested class of service for each of the applications. Applications specifying a class of service typically want to ensure at least a minimum level of processing responsiveness or throughput from a computing facility utility during one or more different dates or time periods. Each class of service provides different degrees of assurance that the performance will occur as scheduled and with the level of efficiency desired. In one implementation, four different types of class of service can be specified including: a static class of service, a guaranteed time varying class of service, a predictable best effort class of service and best effort class of service. Details on these class of service types and their effect on operating the computer utility facility are described in further detail later herein. 
   Monitoring component  334  creates an audit trail associated with requests to acquire and/or release resources from resource pools and the overall computing utility facility. Detailed data gathering operations programmed into monitoring component  334  create an audit trail with emphasis on facts related to operation of the application in conjunction with a requested resource. For example, monitoring component  334  can specify inclusion of variable length descriptive information, failure cause information and other information useful in analyzing resource distribution, utilization and other interactions with the system. 
   Knowledge management component  336  is an overall analysis module that exploits information from monitoring component  334  as well as results from other components in system  300 . The services provided by knowledge management component  336  include access control to data elements in system  300  and security implementations for system  300 . For example, the services provided by knowledge management component  336  include: categorizing applications into different workload classes, maintaining different application profiles automatically, anticipating future application demands for resources in a computing utility facility, and projecting failure rates for certain resources and providing capacity planning scenarios for the operator of the computing utility facility. 
     FIG. 4  is a flowchart diagram providing the operations for governing access to resources in a computer utility facility in accordance with one implementation of the present invention. Initially, a customer submits a demand profile associated with an application that identifies a class of service and the resources required during one or more demand cycles ( 402 ). The demand profile optionally also includes underlying raw trace data used to derive the entries in the demand profile. As previously described, implementations of the present invention use the demand profiles to create a polycyclic demand for resources delivered with a class of service, manage any overbooking of resources and ensure the availability of resources. Class of service information is also used later when resources are in contention and implementations of the present invention need additional criteria for prioritizing their distribution. 
   In one implementation, the demand profiles can be created empirically through data collection or through various statistical estimation methodologies. For example, the demand profile for one application can include many smaller demand profiles corresponding to different time periods or other cycles of operation used by the application. Because business applications are often run continuously, there may be one demand cycle associated with demand during the week and another demand cycle associated with demand by the application on weekends or other period when the activity is reduced or lessened. Class of service requirements may also vary according to financial or other incentives for running a particular application with a higher degree of efficiency and performance during one time period compared with another time period. For example, a business may request a higher class of performance when customers running an application cannot afford to receive slow or poor performance. If performance is critical, these customers may even be willing to pay a premium in exchange for a more responsive computing facility as specified through an SLA or other contractual obligation. 
   Alternatively, if cyclic profiles are not known in advance, an application requesting resources may allow implementations of the present invention to identify the appropriate demand cycles. For example, monitoring and knowledge management components can be used to learn and report on demand cycles and class of service for one or more applications. This information can be used directly or indirectly to then generate demand profiles useful in subsequent resource reservation requests. 
   Once the demand profiles are provided or derived, implementations of the present invention then admit the application if required resources and class of service can be provided from an available resource pool ( 404 ). The admission process involves comparing the one or more time demand cycles making up the polycyclic demand for a resource with the availability of the resource. To meet class of service requirements, these resources must be delivered to the application with at least the level of service specified. In one implementation, statistical analysis is used to project this information and determine if admitting the application and fulfilling the projected corresponding demand and class of service is feasible in light of demand profiles from the other already admitted applications. The utility can optionally provide a higher or more desirable class of service but depending on the agreement may not be able to charge additional fees. Further details on the admission process using class of service considerations are described in further detail later herein. 
   To further manage potential overbooking, implementations of the present invention may also police requests for resources from the admitted applications to determine if requested resources are within an acceptable range ( 406 ). Before admission, applications provide a demand profile based upon an expected usage of one or more resources while executing an application over a period of time. The demand profile also includes the minimum required class of service specified by the application as previously described. While running business applications and other applications continuously or for long time periods, it is possible that an application may attempt to exceed the boundaries corresponding to the demand profile initially provided by the application upon admission to the computing utility facility. Accordingly, policing individual requests from applications as these applications run helps ensure these applications do not exceed the expected resource usage as specified and used as the basis for their admission. Details on policing operations are described later herein. 
   Despite these attempts to avoid a conflict, occasionally it may be necessary to arbitrate which applications are entitled to a requested but limited resource ( 408 ). Arbitration implemented in accordance with the present invention may be required to provide the resource to one application and deny the resource to other applications contending for the same resource and/or class of service. Consequently, arbitration takes into account the contracted class of service and the corresponding pricing penalties paid by the computing utility facility when the class of service and resource requirements is not met. Further details on the arbitration operations in light of class of service are also described in further detail later herein. Once the application&#39;s request is processed as described, implementations of the present invention assign the available resources to fulfill the request ( 410 ). The resource is released from the application once the request is fulfilled and can be reassigned at a later point in time. 
   Together the results from the admission, policing, arbitration and other operations are monitored and kept for later analysis ( 412 ). The audit trail developed during the monitoring stages assists in understanding the allocation of resources, the request and release of certain resources along with the outcome of each request for resources. For example, the monitoring can track if an application requesting a resource becomes entitled to the resource or is rejected; further monitoring can also reveal details on the resource selected and assigned to an application. These results can be passed directly to the knowledge management component of the present invention or archived for subsequent analysis. 
     FIG. 5  is a flowchart diagram of the operations that combine the multiple demand profiles and class of service requirements in accordance with one implementation of the present invention. This flowchart diagram in  FIG. 5  further describes step  404  from  FIG. 4 . These operations capture both polycyclic demand and class of service requirements for an application running continuously or over a long period of time within a computing utility environment. 
   Initially, implementations of the present invention unfold regular and caveat demand time slots onto a staging calendar according to the submitted demand profiles and class of service requirements ( 502 ). Regular demand time slots generally reoccur on a relatively short time frame while caveat demand time slots occur over much longer periods of times. For example, one set of demand time slots used by an application may repeat during the week while another set of demand time slots occur with a certain demand on the weekends. More occasional events including sporting events or certain holidays can be predicted by entering a demand for resources using the caveat demand time slot. Together, the various types of demand occur at a particular cycle creating the polycyclic behavior associated with the application. 
   Class of service requirements specify the minimum desired level of service an application will accept when receiving a particular requested resource. In one implementation, the demand for the requested resources may be associated with one or more different classes of service in either a static or a time varying manner. These particular classes of service include: (1) a static service delivered by the computing utility at a constant level that does not vary based on time of day or other factors (2) guaranteed time varying service delivered by the computing utility that guarantees (i.e., 100% assurance) access to a certain number of resources according to the particular time slot (3) predictable best effort (PBE) class of service delivered by the computing utility that provides a certain probability or assurance rather than a guarantee (i.e., something less than 100% assurance) that a certain number of resources will be available at the particular probability (4) best effort service delivered by the computing utility that provides resources on an as available basis only; in some cases, the computing utility may even require some previously allocated resources to be returned to the utility on demand when an entitlement is exceeded or at any point in time when a best effort allocation is made. Further details on the various class of service types are described in further detail later herein. 
   In an alternate implementation, calendar based caveats may also be used to vary the particular class of service requirements associated with a resource in a demand profile. These calendar-based caveats allow a demand profile to occasionally also modify the class of service requirements without changing the overall general scheme. For example, an application can specify a first class of service (class of service A) in the demand profile each day of the week with the exception that a second class of service (class of service B) is required on Tuesdays between 2 pm and 4 pm. These caveats allow an application to specify a different class of service on an occasional basis as exceptions to normal service and demand requirements occur. 
   Each of the above implementations unfolds both the regular and caveat based demand profiles onto a staging calendar. The staging calendar is used to determine if the pool of resources associated with the computing utility facility is able to provide the required resources and class of service requested by the application ( 504 ). Resource pools associated with the computing utility facility are probed to determine if the request made by an application can be fulfilled at both the time slot and the minimum desired class of service. 
   Admission operations of the present invention compute whether the sum of resource requirements for all applications across multiple class of service can be supported ( 505 ). In one implementation, the admission operation computes the resources and multiple class of service required by all applications. Calculating the demand for resources and multiple classes of service together allows more sharing between applications and available resources. This enables a computing utility to achieve a higher asset utilization of its resource pools through a more careful allocation of the underlying resources. 
   In an alternate implementation, the computing utility does not make an aggregate determination but instead adds the separate demand and class of service requirements for each individual application. This approach is likely to require more resources than the aggregate solution. Fulfilling individual requests tends to utilize more resources as the sharing of excess resources between applications is less likely to occur. 
   If the resources are available, implementations of the present invention admit an application to the computing utility for further processing ( 505 ). In one implementation, this first involves converting time slot entries from staging calendar to the permanent calendar for scheduling ( 506 ). This conversion can be done by keeping separate staging and permanent calendars or merely changing the status of a time slot entry from being staged or temporary to permanent when the scheduling is complete. Optionally, the present invention can then preallocate resources from the resource pools at the required level of assurance (i.e., class of service) according to entries in the permanent calendar schedule ( 508 ). This latter step would additionally make sure the resources do not subsequently appear available due to race conditions or other applications being processed in parallel by the computing utility. 
   Alternatively, if the resources in the resource pools are not available then it may be possible to accommodate the demand profile by expanding the resource pools to include additional resources ( 510 ). Once the additional resources are added to the pool then the demand profile and associated class of service requirements are compared again to available resources ( 502 ). 
   When no additional resources can be added, the computing utility designed in accordance with implementations of the present invention attempts to fulfill the request by proposing to reduce the class of service for one or more time slots and applications ( 512 ). In one implementation, class of service is reduced for the time slots and applications unable to receive the requested service and gain admission to the computing facility. Alternatively, the class of service (CoS) is reduced for different applications across the operating platform and is not limited to the former set of applications not already admitted to the computing facility. 
   In either case, the application can specify a minimum desired class of service directly in the demand profile based on the level of performance desired by the application. Implementations of the present invention confirm that the class of service reduction proposed by the utility is acceptable by the one or more applications ( 514 ). In one implementation, the application can accept or reject the proposed reduction in class of service through a real-time interface used to admit the application into the computing utility. Alternatively, the application may decide in advance what reductions in class of service and terms and conditions are acceptable or unacceptable. Terms and conditions affected by the proposed reduction in class depend on the particular SLA associated with the application. In some cases, the computing utility would suffer a penalty for reducing the class of service while in other cases a reduction in the class of service would reduce the fees for using the computing utility by the application without imposing additional penalties on the utility. In general, implementations of the present invention would consider the various financial arrangements specified in each application&#39;s SLA and attempt to maximize revenue to the utility by minimizing overall penalties and fee reductions. 
   In the event the proposed lower class of service is not accepted, implementations of the present invention would reject one or more applications from computing facility ( 515 ). Based on the illustrated implementation, this would involve removing requested resources, if any, entered temporarily onto the staging calendar from the demand profile ( 516 ) in preparation for subsequent operations. This would be followed by then rejecting the demand profile and associated application as the resources and requested class of service are not available ( 518 ). 
     FIG. 6  is a schematic diagram illustrating the one or more class of service used in accordance with one implementations of the present invention. As previously described, these classes of service  600  includes: (1) a static service delivered by the computing utility at a constant level that does not vary based on time of day or other factors (2) guaranteed time varying service delivered by the computing utility that guarantees (i.e., 100% assurance) access to a certain number of resources according to the particular time slot (3) predictable best effort (PBE) class of service delivered by the computing utility that provides a certain probability or assurance rather than a guarantee (i.e., something less than 100% assurance) that a certain number of resources will be available at the particular probability (4) best effort service delivered by the computing utility that provides resources on an as available basis only; in some cases, the computing utility may even require some previously allocated resources to be returned to the utility on demand when an entitlement is exceeded or at any point in time when a best effort allocation is made. Further details on the various class of service types are described in further detail later herein. 
   In this example, classes of service  600  arrange the different classes in a pyramid to illustrate a hierarchical arrangement for modifying the class of service. In one implementation, an increase in the class of service goes from best effort  608  to predictable best effort  606  to guaranteed time varying  604  and to static  602 . Conversely, a decrease in the class of service goes from static  602  to guaranteed time varying  604  to predictable best effort  606  and then to best effort  608 . As class of service increases, the performance requirements on the computing utility are more restrictive and less variation in service is tolerated. In comparison, decreasing the class of service is necessarily accompanied by more tolerance or variation. For example, a predictable best effort (PBE)  606  class of service can be specified in accordance within different levels of assurance, for example, ranging from PBE-0.9 to PBE-0.99999. 
     FIG. 7  is a flowchart diagram of the operations used to police requests  406  for resources from admitted applications in one implementation of the present invention. Initially, the policing intercepts all requests for resources from applications admitted to access a pool of resources ( 702 ). The policing operations check that a resource request is within a tolerable range considering the demand profile for the application ( 704 ). These policing operations consider the quantity of resources requested in light of the expected burstiness of the application. Details on the entitlement profiles and the computing utility evaluation of an application&#39;s burstiness are described in further detail later herein. 
   Optionally, policing operations may also confirm that the requested resources are within the expected or designated class of service associated with the application ( 706 ). If the application request for a resource is within the tolerable range for the demand profile and class of service then an indication is provided that the application is entitled to the requested resources ( 708 ). 
   Alternatively, in the event the request is outside of the demand profile or expected class of service for the application, a request is made to the application to adjust the request for resources ( 710 ) and try once again. Implementations of the present invention provide an indication to applications unable to adjust their request for resources that they are not entitled to the requested resources ( 712 ). 
     FIG. 8  is a flowchart diagram further detailing one implementation of the present invention for policing of requests for resources by one or more applications. In particular these operations describe the policing operations for checking that a resource request is within a tolerable range  704  as illustrated and described previously with respect to  FIG. 7 . 
   In this implementation, the policing operation of the present invention acquires an entitlement profile to determine the application&#39;s actual entitlement to a resource ( 802 ). Policing generally helps monitor resource usage on the computing facility and recapture costs when the resource requests exceed the computing utilities expected demand for the particular application. The entitlement profile is a negotiated set of parameters and, in certain cases, operating procedures for dealing with the operational and financial consequences of these types of demands. This is necessary in the event one or more applications experience a sudden demand for resources outside the nominal demand profile provided upon admittance to the computing utility facility. 
   Typically, the entitlement profile is negotiated along with the SLA when the applications are analyzed and admitted to the computing utility facility. As previously described, the entitlement profile augments the overall demand profile associated with each application and provides a more detailed operational characteristics of the application. In one aspect, the entitlement profile facilitates characterizing the burstiness of the application given different periods or windows of time. To derive this information, one implementation of the present invention analyzes and uses detailed trace data reflecting historical operation of the application and use of resources in various time periods or windows as described and used later herein. 
   With the entitlement profile, the policing operation identifies an entitlement value based upon a sliding window over a portion of the aggregate time, a burst loading factor and the demand profile ( 804 ). The entitlement value serves as a metric for determining whether a particular application is entitled to the requested resources in the particular window. The entitlement value is proportional to the burst loading factor and the past resource usage derived from historical trace data for the application. If the application is very erratic or bursty in the given window size, the burst loading factor is large to allow the application to make larger requests during the particular time window. Conversely, if the application resource usage is relatively constant and not as bursty then a smaller burst loading factor is used thus limiting the size of requests in the particular window. 
   For example, the entitlement value determination typically selects a sliding window size (W) that is a fraction of the aggregate time period (T) during which an aggregate entitlement of the resources (D) exists. The burst loading factor is determined for each window size and provides a historical measure of the application&#39;s tendency to be bursty during this particular interval. During a sliding window (W) of approximately ½ T, a very bursty application may have an 80% burst loading factor and be entitled make a request up to 80% of D during W. However, the less bursty application during the same sliding window (W) of approximately ½ T would have a 60% burst loading factor instead allowing them to make requests of only 60% of D during window W. On the computing utility side, the more bursty applications having the higher burst loading factor would generally be more costly to run as they typically require more resources. 
   Next, the policing operation determines whether the actual request for resource exceeds entitlement value for the particular sliding window ( 806 ). Each request is checked against a sliding window size and entitlement values to help ensure the application does not exceed the projected amount of resources made available to the application. Different windows sizes and corresponding entitlement values are processed in this manner to cover different possible patterns of resource usage during the overall aggregate time period (T). 
   As previously described, the entitlement value can be derived in part from the trade data and information in the demand profile values submitted with the application. As a refinement, the accuracy of the entitlement value is further evaluated in consideration of a confidence interval that bounds the actual entitlement value calculated. This confidence interval helps the computing utility facility determine when the resource request should be fulfilled or denied. When the number of samples provided in the demand profile is large and/or the application demand data is very accurate then the confidence interval is relatively small and the entitlement value is more reliable. Conversely, fewer samples in the demand profile of the application would result in a much larger confidence interval. Larger confidence intervals allows the computing utility to reject a resource request more readily as the entitlement values calculated are inherently less accurate (i.e., could be larger or smaller). This helps the computing utility reject resource requests falling outside the confidence interval without suffering SLA, contractual or other penalties for doing so. 
   The application&#39;s request for resources is not granted when the request exceeds the entitlement value in view of the sliding window ( 808 ). In general, the policing operation denies the request for resources if any one of the different window size and entitlement value combinations should deny the request for resources. For example, if the request exceeds the entitlement value associated with a window (W) of size ½ T the request is denied even if a previous comparison against an entitlement value for a window (W) of size ¾ T allowed the request. 
   At least two events may occur when the computing utility facility does not fulfill the application&#39;s request for resources. In one case, the resource requested is denied or throttled. This means the application is not granted the request and must perform the subsequent operations without additional resources as requested. Alternatively, the computing utility facility may also determine that the application has a resource but has utilized the resource for a period of time exceeding the time period contemplated by the utility when the resource was originally granted. In this latter case, the computing utility facility would reclaim or “clawback” the previously granted resource due to the application not returning the resource on it&#39;s own accord. This clawback operation has no negative financial impact on the utility as the application has exceeded the usage period; in some cases the clawback operation may actually result in additional fees to the computing utility facility and depends on the particular SLA or contractual arrangement associated with the application. 
   Alternatively, the policing operation compares the request against additional sliding windows and entitlement values if prior entitlement values do not serve to deny the requested resource ( 810 ). The number of sliding windows used to qualify the entitlement depends on the implementation of the policing function of the present invention. In some cases, only two entitlement value and sliding window sizes are used for the determination before the application receives indication and is granted right to the requested resource ( 812 ). For example, a first sliding window (W) of size T is used and a second sliding window of approximately ½ T is used for purposes of policing the requests. In other cases, the policing operation identifies several additional or alternate sliding window and entitlement value combinations ( 814 ) and iteratively repeats the above operations until completion. 
     FIG. 9  is a schematic diagram of various time periods and sliding windows used to determine an entitlement value in accordance with implementations of the present invention. In this diagram, sliding windows are illustrated in the context of an annual calendar  902 , a month calendar  904  and a weekly calendar  906 . By way of example, this diagram illustrates examples of different sliding windows used to allocate resources to applications. These various sliding window examples may span various time intervals and depends on the terms negotiated between the computing facility utility and the application. In this example, annual calendar  902  highlights a set of intermittent sliding windows that occur on the last work week of each month. Month calendar  904  illustrates an intermittent type of sliding window that covers a time interval occurring the first work day in each week. The sliding window on weekly calendar  906  provides both a contiguous entitlement window covering several hours on particular workday and an intermittent entitlement window covering the same time interval for each day in a work week. 
     FIG. 10  is flowchart diagram detailing the operations for arbitration of resources  408  in accordance with one implementation of the present invention. As previously described, some cases may arise where multiple applications admitted to the computing utility facility have contention for one or more of the same resources. In one implementation, the present invention detects a conflict in providing requested resources to two or more admitted applications both ostensibly entitled to the resources ( 1002 ). Each of the applications is entitled to the resources as they have made a request within their respective demand profile, class of service and entitlement profile. However, the requested resource is in limited supply and cannot be assigned to both applications without causing a conflict or contention. 
   To resolve this dilemma, one implementation of the present invention determines if at least one application&#39;s request for resources can be deferred until a later time ( 1004 ). In one implementation, deferring the application has no operational impact on the application and does not cause the computing facility to lose revenue or incur any penalties directly or indirectly for deferring the selected application. The selected application is then instructed to delay a random period of time before resubmitting the request for the resources thereby allowing another application to receive the resource requested ( 1006 ). 
   If no application can readily defer the request for resources, an alternative solution identifies a method for providing the limited resources to only selected applications ( 1008 ). In one implementation, the requested resources in contention are allocated to the entitled applications on a first-come-first-served basis ( 1010 ). Yet another implementation allocates resources according to economic and class of service factors ( 1012 ). 
   In one implementation, the present invention selects the allocation of resources in a manner that minimizes penalties and financial loss to the computing facility. This operation involves comparing the class of service associated with one or more applications and the associated penalties specified in the application&#39;s corresponding contract or SLA. For example, an application with a static class of service specified in the SLA may generate larger penalties against the computing facility than a similar application operating on a best efforts class of service. Accordingly, one implementation would rank the two or more admitted applications entitled to receive the limited resources according to potential economic penalties imposed upon the computing utility facility. 
   Based upon this ranking, the present invention would select one or more admitted applications to not receive the limited resources in order to minimize the economic penalty to the computing utility facility. For example, the class of service and corresponding SLA would influence implementations of the present invention to favor providing the resources to the application with the higher class of service (e.g., the static class of service) over the lower class of service (e.g., the best effort class of service). Of course while this is only an example, alternate implementations using different classes of service and terms and conditions in the SLA or other contractual arrangement would also be driven by minimizing loss or maximizing gain to the computing facility and therefore operate in a similar manner. 
     FIG. 11  is schematic diagram for updating a demand profile for an application as the application&#39;s resource demand exhibits a trend and changes over time. The computing utility can use trending to modify the demand profile for an application over time and thereby improve the accuracy and usefulness of the demand profile in the computing utility. Instead of the demand profile remaining static and constant in the computing utility, trending performed in accordance with the present invention modifies the demand profile thereby reflecting incremental changes in the resource demand. 
   As previously described, each application supplies a demand profile describing the application&#39;s projected demand for resources ( 1102 ). Depending on the circumstances, the demand profile is generally provided along with the application during the computing facility admission operation. If the application has already been admitted, the demand profile associated with the application has already been accepted into the computing utility yet may need to be updated due to changes occurring over time in the application&#39;s resource demand. Each demand profile is described as a series of time slots having well-defined durations of time and associated with a per-slot resource demand value. The demand values can be described using various statistical models including a mean resource demand, a mean resource demand augmented by higher moments of demand, a resource demand in terms of a probability mass function or probability density function. 
   In the event the resource demand is not constant, a trending specification and resource demand for the application is used to potentially modify the demand profile ( 1104 ). In one implementation of the present invention, the trending specification information includes information provided with the application describing expected trends in growth as the application operates within the computing facility. These growth expectations can be characterized in days, weeks, months, quarters, annually and other intervals of time and used to update the demand profile at corresponding frequencies. In addition to the expectations associated with the application, the trending specification information may also include observed data collected as the application actually uses resources from the computing facility over time. For example, resource demand data can be collected and aggregated for each month an application is operating within the computing utility. 
   As will be described in further detail later herein, the trending specification and resource demand data is then used to perform a demand profile trend analysis ( 1106 ). This involves carefully analyzing the data collected as the resource demands change over time and in light of the customer&#39;s or application&#39;s trending specification. The computing utility uses the resulting application trending information to determine the most likely time slots the application will occupy and the extent of the resource demand in light of the trend ( 1108 ). This information is used immediately to unfold the resource demand from the application on a staging calendar or permanent calendar if the resource demand can be accommodated ( 1110 ), and then updates the application demand profile ( 1112 ) for future trend analysis. 
     FIG. 12  is a flowchart diagram of the operations associated with trending and updating demand profiles in accordance with one implementation of the present invention. Initially, the computing utility receives a demand profile associated with an application that identifies resources and class of service information ( 1202 ). The demand profile provides a starting point to measure the demand for resources and is subject to modification over time as determined by trending information as described later herein. 
   The trending operation typically receives the trending specification information upon admission to the computing utility ( 1204 ). A trend specification conveniently contains the expected trend information indicating, among other things, how often to update the demand profile. For example, it may be desirable to update a demand profile weekly, monthly, every several months or at another more appropriate frequency depending on the application and usage trend. As an adjunct to the update frequency, the actual steps or procedures used to update the demand profile are included and/or described by a trend function. For example, the trend function may indicate updating the demand profile when making resource reservations in the staging calendar. From the onset, the trend specification and trend function along with other trending information may cause the resource reservations to vary over time. The combination of information in the trending specification and demand profile are used to make more accurate projections of resource usage by the application in the computing utility. Trending information is considered upon admission to the computer facility and continues to be evaluated as the application uses varying amounts of resources. 
   In addition to the supplied trending data and projections made therewith, the current demand profile in the computing facility is also evaluated as the computing facility and system executes. In some cases, the observed data may indicate an actual trend that is distinct from the expected trend described by the initial trending data. For example, an application using greater or fewer resources may exhibit an actual trend significantly different from the expected trend submitted with the original reservation. For at least this reason, trace data is collected during one or more demand cycles as the system executes the application and used to evaluate accuracy of expected trends and trending information. 
   The frequency in which trending is applied to the demand profile largely depends on the frequency associated with the trending. For example, a demand profile specifying one hour time slots may further include trending specifications that operate at weekly or monthly intervals. Accordingly, a trending function based on the trending specification may be performed at corresponding weekly, monthly or other intervals as appropriate. In an alternate implementation, the trending specification is not provided immediately and instead created as the system executes and observes trends. This alternate implementation does not require the trending information upon admission but instead gathers the information during execution for use with subsequent resource reservations. 
   Many other approaches to trending are also possible through different combinations of provided trending data and trending information collected during system execution. For example, the trending specification information may result from collecting observed data as the application uses resources from the computing utility as well as raw data or expected data produced by the customer for use by the computer facility. The computing facility uses both the observed data and/or customer expectations, provided upon admissions, to model changes in the resource demand and to anticipate an application&#39;s expected growth. Functions used to characterize the demand profile or changes in the demand profile may detect the observed data and use polynomial, exponential, linear or other models to predict these changes. 
   Once the trending specification and trends are identified or received and modeled, implementations of the present invention then determine if a submitted or existing demand profile needs updating ( 1206 ). Updating the demand profile based upon trends extends the time of use for each demand profile and accommodates changes in business conditions and general operation of the application. In one implementation, the trending information specifies updating the demand profile at fixed intervals or periods and based upon the trend itself. As previously described, the frequency in which trending is applied to the demand profile largely depends on the trend itself. For example, a demand profile may be updated weekly based upon a trend purported to be changing on a weekly basis. Conversely, if the trend does not indicate updating the demand profile then the computing facility continues operating the application in the computing utility without changing current demand values in the respective demand profile ( 1208 ). 
   Alternatively, the trend may indicate to apply the trending specification to update values for each time slot in the demand profile ( 1210 ) as it is unfolded onto a calendar. The trends are typically expressed relative to instances of cycles or caveats specified in the demand profile. Models for updating the values in each time slot apply curve fitting methodologies to the observed data collected in light of the application&#39;s expected growth. This information is then used to generate statistical measurements associated with the resulting curves and predict trends in the resource demand. For example, a trend associated with an application may be used to justify an incremental increase in the mean demand or standard deviation associated with a demand slot in the demand profile being updated. 
   If a probability mass function represents the resource demand in the demand profile, updating the demand profile can depend on further factors. For example, determining whether to update a peak or minimum resource demand described by the probability mass function can correspond directly to a trend identified using the raw trace data collected on the application. Alternatively, an updated peak or minimum resource demand can depend on observed ratios identified between the peak resource demand and mean resource demand as well as ratios between the minimum resource demand and mean resource demand. 
   The probability mass function representing the demand profile can also be updated using optimization techniques. In this approach, updates to the probability mass function include finding probabilities for revised sample values that match the revised mean value while minimizing the error between the resulting standard deviation and the revised standard deviation. Further details on the application of optimization to updating the probability mass function in a demand profile are described in detail later herein. 
   Once the demand profile is updated, a determination is made whether the updated time slot values differ significantly from the initial resource projections done at admission ( 1212 ). In one implementation, the resource projections are based on resource usage information within both the demand profile and the trending specification. If the projected resource demand values from the demand profile and trending specification are significantly different, the application is readmitted to computing facility with updated demand profile ( 1214 ). By going through the admission process once again, the computing facility can better ascertain the resource demand needs of the application. This helps ensure that the computing facility has allocated resources efficiently and has properly charged for the resources being provided. Alternatively, if the resource demand values remain within bounds considered upon initial admission, the application and the updated demand profile continue operating in the computing facility ( 1208 ). This latter approach allows the application to use the updated demand profile without the additional overhead associated with going through the admission process again. In either the former or latter approach, the updated demand profile may affect other operational aspects in other areas of the computing facility. For example, the updated demand profile may be used to recalculate entitlement profiles associated with various applications and their subsequent policing based upon these profiles. This can further affect the computing facility&#39;s throttling or limiting resource allocation when an application requests more resources than specified in its entitlement profile or clawback or taking back resources when an application does not release resources in a timely manner consistent with the entitlement profile and allocation scheme. 
   As previously mentioned, optimization techniques can be used to drive trending analysis for application demand profiles. For example, an application&#39;s time varying demand for a resource X(t) can generally be represented by the following relationship:
 
 X ( t )= m ( t )+ n ( t )   (1.1)
 
Where:
         X(t) represents overall demand for a particular resource;   m(t) corresponds to a repeatable/cyclic pattern of the demand; and   n(t) corresponds to a non-deterministic portion of resource demand.       

   In the general representation of the resource demand, At) is the repeatable or deterministic portion of the trend and represents the resource demand the application uses cyclically. The deterministic portion of the trend m(t) may have multiple sub-components operating at different frequencies detectable using Fourier Transforms. For example, if T is the common denominator of the cyclic sub-components, then m(t) satisfies m(t)=m(t+T). 
   One can model the non-deterministic component n(t) of the demand profile in several ways. In one implementation, the non-deterministic component n(t) is modeled as a zero-mean random process and considered “white noise” when n(t) are mutually independent random variables. Provided n(t) obeys a normal distribution, the n(t) component is further considered Gaussian white noise. In yet another implementation, however, the non-deterministic component n(t) is not restricted to Gaussian white noise or even white noise as long as n(t) is considered periodic and n(t) and n(t+T) are drawn from the same distribution. 
   In practice, a probability mass function (pmf) can be developed to represent the demand profile for the application X(t). This approach does not separately represent the deterministic m(t) and non-deterministic n(t) portions as previously described. Instead, the pmf assumes X(t) is an integer random variable and characterizes the resource demand at time t as a series of possible values X(t):{x i (t):i=1 . . . , N(t)} and represented as:
 
 X ( t ):{( x   i ( t ), p   i ( t )): i= 1  . . . , N ( t )}  (1.2)
 
Where:
         x i (t) is one possible value of X(t) at time t;   p i (t) is the probability of the value x i (t) occurring at time t; and   i=1 . . . ,N(t) is the possibilities for X(t) at time t.       

   If desired, this framework could be used to represent the deterministic portion of the resource demand, m(t), as the mean value of the pmf as a function of time t. Similarly, a standard deviation s(t) could also be computed from the pmf values described previously. 
   To determine the effect of trending upon the demand profile, assume an independent trending function l(t) operates on X(t) in the pmf and reflects the application&#39;s changing resource demand. The scaling of X(t) can be done either in an additive manner, a multiplicative manner, a combination of these or any other mathematical functions that best represent this growth. 
   In the event the growth is additive, the mean value demand m(t) grows linearly with time while the variable component s(t) remains relatively stable. For example, a trend associated with an application may predict a weekly increase in processing corresponding to approximately “1 CPU” for each increase. Accordingly, the model for this trend would be described as:
 
 X ′( t )= X ( t )+ l ( t )   (1.3)
 
Where:
         X′(t) is the updated pmf value with trend increase l(t) at time t;   X(t) is the initial pmf value before trend increase l(t) at time t; and   l(t) is a step function corresponding to a weekly increase of 1 CPU resource or other resource at time t.       

   When the growth is multiplicative then the model is represented by the following relationship:
 
 X ′( t )= X ( t )* l ( t )   (1.4)
 
Where:
         X′(t) is the updated pmf value with trend increase l(t) at time t;   X(t) is the initial pmf value before trend increase l(t) at time t; and   l(t) is a growth function with a growth rate of r per unit time, i.e.,
 
 l ( t )=(1 +r ) M    (1.5)
 
Where:
   M is the period growth occurs for a given time t.       

   Compared with equation (1.3), when r=0.1 the multiplicative relationship in equation (1.4) indicates that the demand for processing or other resource is increasing about 10% per unit time compounded. This can be further interpreted as causing both the mean demand value m(t), and the standard deviation, s(t), of the demand value to grow at a rate of approximately 10% per unit time. 
   In view of the multiplicative growth, the revised demand profile has a pmf as follows:
 
 X ( t ):{( x   i ( t )* l ( t ), p   i ( t )): i =1  . . . ,N ( t )}tm (1.6)
 
Where:
         x i (t) is one possible value of X(t) at time t;   p i (t) is the probability of the value x i (t) occurring at time t;   l(t) is a growth function with a growth rate of r per unit time, defined in (1.5).   i=1. . . , N(t) is the possibilities for X(t) at time t.       

   A more general case could also be considered in light of the previous calculations. For example, assume we have a trend forecasting an increase in the resource demand that results in a revised mean demand value m′(t), a revised standard deviation demand value s′(t) and revised minimum and maximum sample values x min  and x max  respectively. Letting N 1 =x max −x min +1 be the new number of samples we can model the revised demand profile with a pmf determined by setting x 1 =x min ,x 2 =x min +1, . . . , x N     1   =x max  and solve the following optimization problem: 
                   Minimize   ⁢              ∑     i   =   1       N   1       ⁢         (         x   i     ⁡     (   t   )       -       m   ′     ⁡     (   t   )         )     2     *       p   i     ⁡     (   t   )           -         s   ′     ⁡     (   t   )       2            ⁢           ⁢   subject   ⁢           ⁢   to   ⁢     :       ⁢     
     ⁢         (   i   )     ⁢           ⁢       ∑     i   =   1     N     ⁢         x   i     ⁡     (   t   )       *       p   i     ⁡     (   t   )             =           m   ′     ⁡     (   t   )       ⁢           ⁢     and   ⁢     
     (   ii   )     ⁢           ⁢       ∑     i   =   1     N     ⁢       p   i     ⁡     (   t   )           =       1   ⁢           ⁢     and   ⁢     
     (   iii   )     ⁢           ⁢       p   i     ⁡     (   t   )         &gt;=   0                 (   1.7   )               
Where:
         x i (t) is one possible value of X(t) at time t;   m′(t) is the revised mean value m(t) of the pmf as a function of time t;   s′(t) is the revised standard deviation of the pmf as a function of time t;   p i (t) is the probability of the value x i (t) occurring at time t; and   N(t) is the number of possibilities for X(t) at time t.       
   Provided N 1  is greater than or equal to 3, the conditions (i), (ii) and (iii) in Equation (1.7) ensure both the probability values are valid and expected mean value as a function of time t is m′(t). Further, the equation (1.7) minimizes the error in the standard deviation calculation. The equation (1.7) is a quadratic program capable of being solved in several different ways. For example, one implementation for solving the quadratic program includes creating a grid of possible values on the interval from [0,1] and then searching through permutations of the p i (t) values to find an optimal solution. 
   While examples and implementations have been described, they should not serve to limit any aspect of the present invention. Accordingly, implementations of the invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. Apparatus of the invention can be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a programmable processor; and method steps of the invention can be performed by a programmable processor executing a program of instructions to perform functions of the invention by operating on input data and generating output. The invention can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. Each computer program can be implemented in a high-level procedural or object-oriented programming language, or in assembly or machine language if desired; and in any case, the language can be a compiled or interpreted language. Suitable processors include, by way of example, both general and special purpose microprocessors. Generally, a processor will receive instructions and data from a read-only memory and/or a random access memory. Generally, a computer will include one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. Any of the foregoing can be supplemented by, or incorporated in, ASICs. 
   While specific embodiments have been described herein for purposes of illustration, various modifications may be made without departing from the spirit and scope of the invention. For example, tables are provided describing one or more demand cycles for a particular resource or pool of resources however the values in these tables are only examples and the organization and scope of information is intentionally limited to illustrate the example. In practice, demand information and corresponding resources could be contained in many tables or databases and may include many details about the resources, class of service, the demand cycles and other demand details. Accordingly, the invention is not limited to the above-described implementations, but instead is defined by the appended claims in light of their full scope of equivalents.