Patent Publication Number: US-6990072-B2

Title: Method and apparatus for arbitration scheduling with a penalty for a switch fabric

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present invention is related to following applications: “Method and Apparatus Parallel, Weighted Arbitration Scheduling for a Switch Fabric” application Ser. No. 09/928,509, and “Method and Apparatus for Weighted Arbitration Scheduling Separately at the Input Ports and the Output Ports of a Switch Fabric” application Ser. No. 09/928,533 both of which are incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   The present invention relates generally to telecommunication switches. More specifically, the present invention relates to parallel, weighted arbitration scheduling for a switch fabric (e.g., an input-buffered switch fabric). 
   Known switch fabrics with crossbar architectures exist where data cells received on the multiple input ports of the switch are sent to the various output ports of the switch. Scheduling techniques ensure that the data cells received from different input ports are not sent to the same output port at the same time. These techniques determine the temporary connections between input ports and output ports, via the switch fabric, for a given time slot. 
   Scheduling techniques can be evaluated based on a number of performance requirements to a broad range of applications. Such performance requirements can include, for example, operating at a high speed, providing a high throughput (i.e., scheduling the routing of as many data cells as possible for each time slot), guaranteeing quality of service (QoS) for specific users, and being easily implemented in hardware. Known scheduling techniques trade one or more performance areas for other performance areas. 
   For example, U.S. Pat. No. 5,500,858 to McKeown discloses one known scheduling technique for an input-queued switch. This known scheduling technique uses rotating priority iterative matching to schedule the routing of data across the crossbar of the switch fabric. When the data cells are received at the input ports in a uniform manner (i.e., in a uniform traffic pattern), this known scheduler can produce a high throughput of data cells across the switch fabric. When the data cells are received at the input ports, however, in a non-uniform manner more typical of actual data traffic, the throughput from this known scheduling technique substantially decreases. 
   Thus, a need exists to provide a scheduling technique that can perform effectively for multiple performance requirements, such as for example, operating at a high speed, providing a high throughput, guaranteeing QoS, and being easily implemented in hardware. 
   SUMMARY OF THE INVENTION 
   Arbitration for a switch fabric (e.g., an input-buffered switch fabric) is performed. The switch fabric has a set of ports. Each port from the set of ports is associated with its own set of links. The set of ports includes a first port and a second port. A link is selected from the set of links associated with the first port based on a weight value associated with each remaining link associated with a candidate packet and being from the set of links associated with the first port. A first penalty for a weight vector entity associated with the first port is determined by based on a weight value associated with each link from a first subset of links from the set of links for the first port. Each link from the first subset of links is not associated with a candidate packet. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  illustrates a system block diagram of a switch, according to an embodiment of the present invention. 
       FIG. 2  shows a system block diagram of the scheduler shown in  FIG. 1   
       FIG. 3  shows a flowchart of an arbitration process, according to an embodiment of the present invention. 
       FIG. 4  shows a system block diagram of a grant arbiter, according to an embodiment of the present invention. 
       FIG. 5  shows a system block diagram of an accept arbiter, according to an embodiment of the present invention. 
       FIG. 6  shows elements related to an example of a grant step of arbitration within a switch, according to an embodiment of the present invention. 
       FIG. 7  shows elements related to an example of an accept step of arbitration based on the example shown in  FIG. 6 . 
       FIG. 8  shows a system block diagram of a scheduler, according to another embodiment of the present invention. 
       FIG. 9  shows an example of a link map between input ports and output ports based on two different arbitration decisions for a given time slot. 
   

   DETAILED DESCRIPTION 
   Embodiments of the present invention relate to parallel, weighted arbitration scheduling for a switch fabric. The scheduling can be performed at a set of ports for a switch fabric, for example, at a set of input ports and/or a set of output ports. Each port from the set of ports has its own set of links. On a per port basis, a subset of links from the set of links associated with that port is determined. Each link from the determined subset of links for that port is associated with a candidate packet. Each link from the set of links for that port is associated with a weight value. On a per port basis, a link from the determined subset of links for that port is selected based on the weight value for determined subset of links for that port. 
   A term “link” can be, for example, a potential path across a crossbar switch within the switch fabric between an input port and an output port. In other words, a given input port can potentially connected to any of many output ports within the crossbar switch. For a given time slot, however, a given input port will typically be connected to at most only one output port via a link. For a different time slot, that given input port can be connected to at most one output port via a different link. Thus, the crossbar switch can have many links (i.e., potential paths) for any given input port and for any given output port, although for a given time slot, only certain of those links will be activated. 
   A link is associated with a candidate packet when a packet is buffered at the input port for that link (e.g., buffered within a virtual output queue associated with that input port and the destination output port). Note that although the term “candidate packet” is used in reference to data queued at the input port, the other types of data such as cells can be considered. 
   The term “weight value” can be, for example, a value associated with a link based on a bandwidth-reserved rate assigned for that link. In other words, a bandwidth can be allocated to different links within the switch fabric based on the reserved rates of those links. In such an example, the weight value for each link can be updated in every time slot according to the reserved rate, the last scheduling decision and a penalization for non-backlogged, high weight-value links. 
   The scheduling techniques described herein can be considered as to three aspects. First, the scheduling techniques (or arbitration techniques) can combine parallel arbitration (among the set of input ports and/or among the set of output ports) with weighted arbitration. In other words, scheduling can be performed among the output ports in parallel and/or among the input ports in parallel while also being based on weight values for the links being considered for scheduling. 
   Second, the scheduling techniques can consider weighted values of the links separately from the perspective of the input ports and from the perspective of the output ports. Thus, a given link between its associated input port and output port has two different weight values (one from the input port perspective and one from the output port perspective) that are maintained separately by the respective input port and output port. 
   Third, the scheduling techniques can assess a penalty for non-backlogged links having a relatively high weight value. Thus, for a given port, any associated links without a candidate packet and having a weight value greater than the weight value of the link selected during arbitration can have their respective weight value penalized. 
     FIG. 1  illustrates a system block diagram of a switch, according to an embodiment of the present invention. Switch fabric  100  includes crossbar switch  110 , input ports  120 , output ports  130  and scheduler  140 . Crossbar  110  is connected to input ports  120  and output ports  130 . Scheduler  140  is coupled to crossbar switch  110 , input ports  120  and output ports  130 . 
   As shown for the top-most input port  120  of  FIG. 1 , each input port  120  has a set of queues  121  into which packets received at the input port are buffered. More specifically, each queue  121  is a virtual output queue (VOQ) uniquely associated with a specific output port  130 . Thus, received packets (each designating a particular destination output port) are buffered in the appropriate VOQ for its destination output port. 
   In general, as packets are received at the input ports  120 , they are subsequently routed to the appropriate output port  130  by the crossbar switch  110 . Of course, packets received at different input ports  120  and destined for the same output port  130  can experience contention within the crossbar switch  110 . Scheduler  140  resolves such contention, as discussed below, based on an arbitration (or scheduling) process. 
   Scheduler  140  uses a parallel, matching scheme that supports rate provisioning. Using this rate-provisioning scheme, scheduler  140  is capable of supporting quality of service (QoS) in traffic engineering in the network (to which switch  100  is connected; not shown). In addition, scheduler  140  provides a high throughput in the switch fabric. 
   Note that input line cards (coupled to the switch fabric  100  but not shown in  FIG. 1 ) can perform the scheduling and intra-port rate-provisioning among all flows that are destined to the same output port. The switch fabric  100  can operate on a coarser granularity and can perform inter-port rate provisioning, and can consider the flows that share the same input/output pair as a bundled aggregate flow. In this way, the number of micro flows is seamless to the rate-provisioning scheme used by the switch fabric  100  and its complexity is independent of the number of micro-flows. 
   Generally speaking, scheduler  140  performs three steps during the arbitration process: generating requests, generating grants and generating accepts. The grant and accept steps are carried out according to the reserve rates of the links associated with the specific input ports  120  and output ports  130 . To keep track of the priorities of different links, scheduler  140  assigns a weight value (or credit value), for example, to every link at every port. 
   In other words, a given input port  120  can be associated with a set of links across crossbar switch  110 , whereby the given input port  120  can be connected to a set of output ports  130  (e.g., every output port  130 ). Similarly, a given output port  130  is associated with a separate set of links across crossbar switch  110 , whereby the given output port  130  can be connected to a set of input ports  120  (e.g., every input port  120 ). Scheduler  140  can be configured so that, for example, a link with a higher weight value has a higher priority. A weight vector can represent the weight values for the set of links associated with a given port. In other words, a given link can have an associated weight value; a set of links for a given port can have an associated weight vector, where the weight vector comprises a set of weight values. 
   The weight vectors can be represented mathematically. More specifically, a weight vector, i.e.,  CI     i       (n)=(CI 1   i (n), . . . , CI N   i (n)), can be assigned to input port i, and similarly, a weight vector, i.e.,  CO     j       (n)=(CO 1   j (n), . . . , CO N   j (n)), can be assigned to output port j, where n is the time index. The kth entry (i.e., the kth weight value), where 1≦k ≦N, of every weight vector corresponds to the kth link of the associated port. 
   The weight values associated with the links are updated by scheduler  140  according to reserved rates of the links and last scheduling decision. In other words, for each time slot, the weight value associated with every link is increased by the link&#39;s reserved rate and decreased when the link is served (i.e., when that link is selected during the arbitration process so that a packet is scheduled for transit via that link). Thus, the weight value of a link indicates how much service is owed to that link. Said another way, the weight value indicates the extent to which a given link is given priority over other links where that priority increases over time until the link is serviced. The reserved rates of the links can be predefined and/or can be adjusted during the operation of the switch. 
   In addition, certain weight values are updated based on a penalty. More specifically, the weight values associated with non-backlogged, high-weight-value links are penalized during a given time slot. In other words, for a given port, any associated links without a candidate packet (buffered at the associated virtual output queue) and having a weight value greater than the weight value of the link selected during the arbitration process have their weight values penalized. The weight values of such links can be, for example, decreased an amount related to the link bandwidth. 
   The operation of scheduler  140  can also be represented mathematically. More specifically, consider input port i and output port j, and suppose that CI max   j (n) and CO max   j (n) are the maximum weights selected in the accept and grant steps, respectively. The reserved rate for link (i,k) is r ik , and A ik (n) is the serving indicator of that link, i.e., 
                 A   ik     ⁡     (   n   )       =     {         1             ⁢     if   ⁢           ⁢     (     i   ,   k     )     ⁢           ⁢   is   ⁢           ⁢   served               0             ⁢   otherwise                     (   1   )             
 
For link (i, k) and at input port i, the penalty for a non-backlogged, high-weight-value link, DI k   i (n), is 
                 DI   k   i     ⁡     (   n   )       =     {         1             ⁢       if   ⁢           ⁢     (     i   ,   k     )     ⁢           ⁢   is   ⁢           ⁢   non   ⁢     -     ⁢   backlogged   ⁢           ⁢   and   ⁢           ⁢       CI   k   i     ⁡     (   n   )         ≥       CI   max   i     ⁡     (   n   )                   0             ⁢   otherwise                     (   2   )             
 
   CO max   j (n) is defined for output port j in a similar way. For link (j, k) and at output port j, the penalty for a non-backlogged, high-weight-value link, DO k   j (n), is 
                 DO   k   j     ⁡     (   n   )       =     {         1             ⁢       if   ⁢           ⁢     (     j   ,   k     )     ⁢           ⁢   is   ⁢           ⁢   non   ⁢     -     ⁢   backlogged   ⁢           ⁢   and   ⁢           ⁢       CO   k   j     ⁡     (   n   )         ≥       CO   max   j     ⁡     (   n   )                   0             ⁢   otherwise                     (   3   )             
 
   Note that DI&#39;s and DO&#39;s specify the weight values that are decremented to penalize the corresponding links. Hence, the weight vector updating rule for the k-th element of input port i and output port j are,
 
 CI   k   i ( n +1) =CI   k   i ( n ) +r   ik ( n )−( DI   k   i ( n ) +A   ik ( n ))
 
 CO   k   j ( n +1) =CO   k   j ( n ) +r   kj ( n ) −( DO   k   j ( n ) +A   kj ( n ))  (4)
 
   Penalizing advantageously limits a non-backlogged link from increasing unboundedly. Without penalization, a weight value for a non-backlogged link could increase unboundedly. Then, when such a link receives a number of packets, the link would distract the service of the other links due to its very high weight value. Moreover, the output pattern of such a scheduler would become very bursty. An alternative approach of reducing the weight value to zero inappropriately introduces a delay on any low-rate links that are non-backlogged most of the time. Thus, the penalizing herein reduces the weight value of a non-backlogged link, for example, by the link&#39;s throughput. 
   In an alternative embodiment, the weight values of the links within a weight vector can be adjusted (either increased or decreased) (separate from the above-described weight vector adjustment). The weight vector can be so adjusted without affecting the overall performance of the scheduler because the rate-provisioning method described herein is based on the relative differences between link weight values, not on their absolute values. 
     FIG. 2  shows a system block diagram of the scheduler shown in  FIG. 1 . As shown in  FIG. 2 , scheduler  140  includes request generator  210 , grant arbiters  220 , accept arbiters  230  and decision generator  240 . Request generator  210  receives input signals from the input ports  120 . Request generator  210  is connected to grant arbiters  220  and accept arbiters  230 . A given grant arbiter  220  is connected to each accept arbiter  230 . The accept arbiters  230  are connected to decision generator  240 . Decision generator  240  provides output signals to crossbar switch  110  and provides feedback signals to grant arbiters  220  and accept arbiters  230 . 
     FIG. 3  shows a flowchart of an arbitration process, according to an embodiment of the present invention. At step  300 , packets are received at input ports  120 . Input signals are provided to request generator  210  based on the received packets. At step  310 , request generator  210  can generate a request for each packet received at an input port  120  based on the received input signals. This request identifies, for example, the source input port  120  and the destination output port  130  for a given packet, and represents a request to transit the crossbar switch  110 . Accordingly, the requests generated by request generator  210  are provided to the appropriate grant arbiters  220 . 
   At step  320 , grant arbiters  220  determine which links have an associated candidate packet based on the requests received from request generator  210 . In other words, request generator  210  generates a request(s) for each link associated with a buffered candidate packet(s). Thus, grant arbiters  220  can determine which links have an associated candidate packet, for example, by identifying for which input port  120  a request has been generated. 
   At step  330 , grant arbiters  220  generate grants based on the requests received from request generator  210 . Grant arbiters  220  can be configured on a per output-port basis or on a per input-port basis. In other words, step  320  can be performed on a per output-port basis or on a per input-port basis. For example, where the grants are determined on a per input-port basis the request associated with a particular input port  120  is sent to the corresponding grant arbiter  220 . In such a configuration, requests from the first input port  120  are sent to the first grant arbiter  220 ; requests from the second input port  120  are sent to the second grant arbiter  220 ; and requests from the n th  input port  120  are sent to the n th  grant arbiter  220 . 
   Alternatively, where grants are determined on a per output-port basis, the request associated with a particular output port  130  is sent to the corresponding grant arbiter  220 . In such a configuration, a request that designates the first destination output port  130  is sent to the first grant arbiter  220 ; a request that designates the second output port  130  is sent to the second grant arbiter  220 ; and a request that designates the n th  output port  130  is sent to the nth grant arbiter  220 . 
   Grant arbiters  220  send an arbitration signal indicative of a grant to the appropriate accept arbiters  230 . More specifically, a given grant arbiter  220  can receive a set of requests (i.e., as few as no requests or as many requests as there are associated links). In the case of a grant arbiter  220  that receives one or more requests, that grant arbiter  220  sends an arbitration signal indicative of a grant to the accept arbiter associated with that grant. 
   At step  340 , accept arbiters  230  generate accepts based on the grants generated by grant arbiters  220 . Accept arbiters  230  be configured on either a per input-port basis or a per output-port basis depending on the configuration of the grant arbiters  220 . In other words, step  340  can be performed on a per input-port basis or on a per output-port basis. More specifically, if step  330  is performed on a per input-port basis by the grant arbiters  220 , then step  340  is performed on a per output-port basis by accept arbiters  230 . Similarly, if step  330  is performed on a per output-port basis by grant arbiters  220 , then step  340  is performed on a per input-port basis by accept arbiters  230 . Once the accepts are generated by accept arbiters  230 , arbitration signals indicating the accepts are provided to the decision generator  240 . 
   At step  350 , decision generator  240  generates an arbitration decision for a given time slot based on the accepts generated by the accept arbiters  230  and provides a signal indicative of the arbitration results for the given time slot to crossbar switch  110 . In addition, the signal indicative of the arbitration results is also sent from decision generator  240  to the grant arbiters  220  and accept arbiters  230  so that the weight values can be updated. The weight values are updated based on which requests were winners in the arbitration process. In addition, certain weight values will be penalized based on this feedback information from decision generator  240 . Weight values are penalized for links having a weight value higher than the link selected but not having a candidate packet buffered at their associated virtual output queues. Said another way, in the cases where a link with a higher weight value than the selected link but no buffered candidate packet (awaiting switching across the crossbar switch  110 ), then that link should be accordingly penalized and its weight value reduced. 
   Note that although the arbitration process has been described in connection with  FIG. 2  for a given time slot, arbitration can be performed multiple times iteratively within a given time slot. In such an embodiment, for example, arbitration winners from prior iterations within a given time slot are removed from consideration and additional iterations of arbitration is performed for the arbitration losers to thereby provide more arbitration winners within a given time slot. 
     FIG. 4  shows a system block diagram of a grant arbiter, according to an embodiment of the present invention. A given grant arbiter  220  includes selection unit  221 , weight-value registers  222 , update unit  223  and logic “and”  224 . Selection unit  221  receives requests R 1j  through R Nj  from request generator  210  and provides an arbitration signal indicative of a grant, G 1j  through G Nj  to an accept arbiter  230 . Although a selection unit  221  typically provides a single arbitration signal indicative of a grant,  FIG. 4  shows the multiple connections from a selection unit  221  upon which a given arbitration signal, G 1j  through G Nj , can be carried to an accept arbiter  230 . 
   The arbitration signal indicative of a grant is also provided to logic “and”  224  from selection unit  221 . Logic “and”  224  also receives a request, R j , and is coupled to update unit  223 . Update unit  223  is also coupled to weight-value registers  222 . Weight-value registers are also coupled to selection unit  221  and provide a signal back to update unit  223 . Update unit  223  also receives a feedback signal indicative of the arbitration results for which an accept, A j , was generated. 
     FIG. 5  shows a system block diagram of an accept arbiter, according to an embodiment of the present invention. A given accept arbiter  230  includes selection unit  231 , weight-value registers  232 , update unit  233  and logic “and”  234 . Selection unit  231  receives a set of arbitration signals each indicative of a grant (i.e., zero or more signals from G i1  through G iN ) from the corresponding grant arbiters  220  (shown in  FIG. 2 ). Selection unit  231  produces at most one arbitration signal indicative of an accept, A i1  through A iN . Selection unit  231  also provides the at most one arbitration signal indicative of an accept to logic “and”  234 . Logic “and”  234  also receives a request R i  and produces a signal to update unit  233 . Update unit  233  provides a signal to weight-value registers  232 . Weight-value registers  232  provide a signal to selection unit  231  and to update unit  233 . In addition, update unit  233  also receives an arbitration signal indicative of an accept, A i . 
     FIG. 6  shows elements related to an example of the arbitration process within a switch, according to an embodiment of the present invention.  FIG. 6  represents the weight values for links across a crossbar switch that connects input ports to output ports. The example of  FIG. 6  is based on the grant step of arbitration being performed on a per output-port basis. 
   As shown in  FIG. 6 , a given output port  1  can be connected across the crossbar switch by links  610 ,  620 ,  630  and  640  to the various input ports  1 ,  2 ,  3  and  4 , respectively. As shown in  FIG. 6 , lines  610 ,  620 ,  630  and  640  have weight-values w 11 =2, w 21 =3, W 31 =1 and w 41 =4, respectively. For the virtual output queues of each input port, the virtual output queues are labeled in  FIG. 6  with an index that indicates the combination of an input port and output port. 
   For example, input port  1  has a virtual output queue labeled Q 11  associated with the output port  1 . This queue has no buffered candidate packets received at input port  1  and destined for output port  1 . Input port  1  also has a series of other virtual output queues associated with the remaining destination output ports, such as for example, Q 12  through to Q 1N . The remaining input ports have similar virtual output queues. For purposes of the illustration in  FIG. 6 , input ports  2  and  3  both have buffered candidate packets in the associated virtual output queues related to output port  1 , i.e., Q 21  of input port  2  and Q 31  of input port  3 . The output ports  1  and  4 , however, do not have candidate packets buffered for the destination output port  1 ; in other words, Q 11  and Q 41  do not have any buffered candidate packets. 
   Following the example of  FIG. 6 , the grant step of arbitration is performed by selecting a subset of links for which each has a candidate packet buffered at the associated virtual output queue. As mentioned above, in this example of  FIG. 6 , only link  620  and link  630  have an associated candidate packet. 
   Next, a grant is determined for the link having the highest weight value from the selected subset of links. In this example, the link  620  has the highest weight-value (i.e., w 21  equal to 3) which is greater than the weight-value for the link  630  (i.e., w 31  equal to 1). Thus, a grant is generated for link  620 . 
   Note that although  FIG. 6  shows an example of the grant step for output port  1 , the other output ports also perform the grant step in parallel. Thus, just as output port  1  produces a grant for input port  2 , the remaining output ports also produce at most one grant for an associated input port (which possibly can also be input port  2 , or some other input port). 
     FIG. 7  shows elements related to an example of the accept step of arbitration based on the example shown in  FIG. 6 . As shown in  FIG. 7 , the accept step is performed on a per input-port basis; this corresponds to the grant step being performed on a per output-port basis. For purposes of clarity,  FIG. 7  shows specific details for only input port  2  while omitting the similar details for the remaining input ports. 
   In the example shown in  FIG. 7 , input port  2  has received a grant for links  710 ,  720  and  730 . The received grant for link  710  corresponds to the grant sent from output port  1  to input port  2  shown in  FIG. 6 . The received grants for links  720  and  730  (received from output ports  2  and  4 , respectively) were generated in parallel with the grant for link  710 , although not shown in  FIG. 6 . 
   During the accept step shown by  FIG. 7 , input port  2  will select the link having the highest weight value, which in this case is the link  730 . In other words, an accept is generated for the link  730  because its weight value (i.e., w′ 24  equal to 7) is greater than the weight value of the remaining links  710  and  720  (i.e., w′ 21  equal to 4 and w′ 22  equal to 3). 
   Note that the weight values for the links from the perspective of the input ports are different than the weight values for the links from the perspective of the output ports. More particularly, each output port and each input port will maintain its own distinct weight vector for its respective links. Thus, the weight-value for a particular link from the output port may have a different weight-value for that same link from the perspective of the input port. For example, note that link  620  (shown in  FIG. 6 ) from the perspective of input port  2  has a different weight value (w 21  equal to 3) than for the weight value for link  710  (shown in  FIG. 7 ) from the perspective of output port  1  (w′ 21  equal to 4). In sum, the weight values for a link from the output port perspective can be separate and independent from the weight values for the link from the input port perspective. Following the examples shown in  FIGS. 6 and 7 , certain weight values are updated based on a penalty. For example, the link between input port  4  and output  1  is penalized. As shown in  FIG. 6 , the link  620  is selected during the grant step because it has the highest weight value (w 21  equal to 3) among the links associated a candidate packet (e.g., links  620  and  630 ). Of the remaining links for output port  1 , links  610  and  640  are not associated with a candidate packet. Of these two links, only link  640  has a weight value (w 41  equal to 4) greater than the weight value of the selected link (i.e., w 21  equal to 3 for link  620 ). Thus, the weight value for the link between output port  1  and input port  4  is penalized. The weight value for this link should be penalized from both the perspective of the output port and the input port. Thus, from the perspective of output port  1 , the weight value w 21 , for link  640  is penalized, for example, by reducing it from a value of 4to 3. In addition, the weight value, w′ 41 , for the link between input port  4  and output  1  from the perspective of input port  4  (not shown in  FIGS. 6 and 7 ) is also reduced, for example, by a penalty of 1. 
     FIG. 8  shows a system block diagram of a scheduler, according to another embodiment of the present invention. As shown in  FIG. 8 , scheduler  440  includes request generator  441 , first-stage arbiters  442 , second-stage arbiters  443 , decision generators  444  and  445 , and matching combiner  446 . Note that  FIG. 8  shows the first-stage arbiters and second-stage arbiters at a first time, t 1 , and at a second time, t 2 . At the first time, t 1 , the first-stage arbiters and second-stage arbiters are labeled as  442  and  443 , respectively; at the second time, t 2 , the first-stage arbiters and second-stage arbiters are labeled as  442 ′ and  443 ′, respectively. First-stage arbiters  442  and  442 ′ are physically the same devices; second-stage arbiters  443  and  443 ′ are physically the same devices.  FIG. 8  shows the transmission of arbitration signals from first-stage arbiters  442  and second-stage arbiters  443  (determined during the first time, t 1 ) to second-stage arbiters  443 ′ and first-stage arbiters  442 ′, respectively (determined during the second time t 2 ). 
   Scheduler  440  operates in a manner similar to the scheduler discussed in reference to  FIGS. 1 through 7 , except that scheduler  440  performs two parallel sets of arbitration. Thus, rather than allowing the arbiters to remain idle during one half of the arbitration process, the arbiters of scheduler  440  operate for a second time during its otherwise idle time within a given time slot (or within a given iteration within the time slot). Consequently, scheduler  440  allows a second arbitration process to be performed in parallel without any additional hardware in the form of additional arbiters; matching combiner  446  is the only additional hardware for this embodiment of a scheduler over the scheduler discussed in reference to  FIGS. 1 through 7 . 
   In other words, the first-stage arbiters  442  and second-stage arbiters  443  perform the grant step of arbitration on a per input-port basis and on a per output-port basis, respectively. This grant step of arbitration can be performed during the first time, t 1 , independently by the first-stage arbiters  442  and second-stage arbiters  443 . Then, the first-stage arbiters  442 ′ and second-stage arbiters  443 ′ perform the accept step of arbitration on a per output-port basis and on a per input-port basis, respectively, based on the grants generated by the second-stage arbiters  443  and the first-stage arbiters  442 , respectively. The accept step can be performed by the first-stage arbiters  442 ′ and second-stage arbiters  443 ′ during the second time, t 2 . Again, note that the first-stage arbiters  442  and  442 ′ are physically the same devices; second-stage arbiters  443  and  443 ′ are physically the same devices. 
   The arbitration signals indicative of accepts are provided to decision generators  444  and  445 , which independently generate separate arbitration decisions. These arbitration decisions are then provided to matching combiner  446 , which provides an integrated arbitration decision for the associated switch fabric. 
   The matching combiner  446  can provide an integrated arbitration decision in a number of ways. For example, matching combiner  446  can determine the matching efficiency for each received arbitration decision (from decision generator  444  and from decision generator  445 ), and then output the arbitration decision having a higher matching efficiency for that time slot. For example, for a given a time slot, the matching combiner  446  might determine that the arbitration decision from decision generator  444  has the higher matching efficiency and select that arbitration decision. Then, for a subsequent time slot, the matching combiner  446  might select the arbitration decision from decision generator  445  if it has the higher matching efficiency. The matching efficiency can be, for example, the percentage of links that are scheduled for a given time slot. 
   Alternatively, matching combiner  445  can alternate each time slot between the two received arbitration decisions. In such an embodiment, the matching combiner  445  can select the arbitration decision from decision generator  444  at one time slot, then select the arbitration decision from decision generator  445  at the next time slot, and so on. 
   In yet another alternative, matching combiner  445  can select different portions of the switch fabric and the corresponding optimal portions of the arbitration decisions. In other words, matching combiner  445  can consider different portions of the switch fabric, and then, for each portion, matching combiner  445  can select the arbitration decision from either the decision generator  444  or decision generator  445  that is optimal (or at least not less optimal) for that portion of the switch fabric. 
     FIG. 9  shows an example of a link map between input ports and output ports based on two different arbitration decisions for a given time slot. The example shown in  FIG. 9  illustrates different links within the switch fabric and the corresponding arbitration decisions. In  FIG. 9 , the solid lines between the input ports and the output ports can represent the arbitration decision from decision generator  444 ; the dotted lines between input ports and output ports can represent the arbitration decision from decision generator  445 . 
   In the example shown in  FIG. 9 , the switch fabric can be considered in three sets of ports: input ports  1  through  3  and output ports  1  through  3 ; input ports  4  through  6  and output ports  4  through  7 ; and input ports  7  through  8  and output port  8 . For the first set of ports, the number of arbitration decisions from decision generator  444  (i.e., the solid lines) exceeds the number of arbitration decisions from decision generator  445  (i.e., the dotted lines). Thus, for the first set of ports, the arbitration decisions from decision generator  444  is optimal. For the second set of ports, the number of arbitration decisions from decision generator  445  (i.e., the dotted lines) exceeds the number of arbitration decisions from decision generator  444  (i.e., the solid lines). Thus, for the second set of ports, the arbitration decisions from decision generator  445  are optimal. For the third set of ports, the number of arbitration decisions from decision generator  444  (i.e., the solid lines) equals the number of arbitration decisions from decision generator  445  (i.e., the dotted lines). Thus, for the third set of ports, the arbitration decisions from either decision generator  444  or  445  are sufficient. 
   Although the present invention has been discussed above in reference to examples of embodiments and processes, other embodiments and/or processes are possible. For example, although various embodiments have been described herein in reference to a switch fabric having an equal number of input ports and output ports, other embodiments are possible where the switch fabric has a number of input ports different from the number output ports. 
   Note that although examples of embodiments of switch fabric discussed above use the rate-provisioning method on both a per input-port basis and a per output-port basis, other embodiments can use the rate-provisioning method on a per input-port basis only or on a per output-port basis only. In such an embodiment, for example, the rate-provisioning method discussed herein can be used for the output ports while another method (e.g., the iSLIP method disclosed in U.S. Pat. No. 5,500,858, which is incorporated herein for background purposes) can be used for the input ports. Such an embodiment can have, for example, a greater number of input ports (e.g., each having a relatively low throughput) than the number of output ports (e.g., each having a relatively high throughput).