Norival R. Figueira and Joseph Pasquale, "An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Transactions on Networking, vol. 3, no. 4, pp. 399--408, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....we consider the design of packet schedulers appropriate for use in networks with a bounded delay service, that is, networks that provide deterministic (i.e. worst case) delay guarantees to all packets on a connection. Many packet schedulers have been considered for use in bounded delay services [7, 8, 13, 15, 29]. The well known Earliest Deadline First (EDF) scheduler has been studied in [7, 11, 12, 18] and is distinguished in that it has optimal efficiency : for a given set of connections, EDF can support delay guarantees that are at least as tight as those provided by any other packet scheduler [11, ....

N. R. Figueira and J. Pasquale. An Upper Bound on Delay for the VirtualClock Service Discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....the performance of best effort traffic. Best effort traffic also uses the slots where guaranteed jitter traffic is not available to take its allotted slot or in the case where the schedule table is a partial permutation table. The following theorem is a special case of the general result in [25]. The proof of the result in our case is straightforward and is proved directly. Theorem 12: If k=1 # k 1, then for all classes k,the LJS algorithm results in 1. Therefore by the above theorem, all connections are (almost) low jitter. Note that some connections may miss their ....

N.R. Figueria and J. Pasquale, "An upper bound on delay for the virtual clock service discipline," IEEE Transactions on Networking,vol.3, August 1995.

....In this section, we evaluate the deterministic bottnd on the end to end delay for a connection in the network controlled by the IRR servers. The delay components of interest in this paper are queueing delay and cell transmission delay suffered at each network node. As done in [5,6] and [17], we assume that the source traffic of connection i at the entrance of the network is 0 (cri ,pl) regular, that is, filtered by a leaky bucket mechanism with drain rate pi, and bucket size cr at the network edge. Based on the traffic characterization derived in the previous section, we ....

N. Figueira and J. Pasquale, "An upper bound on delay for the virtual clock service discipline," IEEE/ACM Trans. Networking, vol. 3, no. 4, pp. 399-408, Aug. 1995.

....the link to real time sessions. 3. 2 Scheduling Discipline We use VirtualClock [19] as the packet scheduling discipline at the base because it is simple and easy to implement, while still providing end to end delay bounds to real time sessions given the reservation of a lower bound of bandwidth [5]. All real time sessions reserved a rate of 32kbits s in the wireless link. We use the two state Gilbert Elliot Markov model [3, 9] which is widely used to describe fading channels. This model describes a stochastic sequential machine (SSM) that generates a binary output sequence. In this ....

N. R. Figueira and J. Pasquale, "An Upper Bound on Delay for the VirtualClock service Discipline," IEEE/ACM Transactions on Networking, Vol. 3, No. 4, pp. 399-408, August 1995.

....authors are with the Department of Computer Science, Texas A M University, College Station, TX 77843. E mail: fswang, dxuan, bettati, zhaog cs.tamu.edu . # # # # # # # # # # # # ############## ####### ### #### # ##### # # # # # # # # # ################## ## ## # ## ### [10, 22] [11, 13, 15, 36] [6, 8, 19, 28] 21, 34, 35] 29, 30] 31] This study Fig. 1. Problem Space and Related Work While deterministic services provide a simple model to the applications, they tend to heavily over commit resources because they account for the worst case scenario. In practical systems, this ....

....the case of providing deterministic services under the intserv model in singlenode networks, various solutions have been reported early on [10] and [22] The case of deterministic services within the intserv model in multi node networks, represented by Vertex B in Fig. 1, has been covered in [11] [13], 15] 36] A number of projects ( 6] 8] 19] 28] address In the following, we will use the term flow to indicate a stream of data between a source and a destination, and the term connection to indicate the virtual circuit that needs to be established to carry the flow. In this paper ....

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Norival R. Figueira, Joseph Pasquale, An Upper Bound on Delay for the VirtualClock Service Discipline, IEEE/ACM Transactions on Networking, Vol. 3. Aug. 1995.

....control and packet scheduling, in terms of end to end delay guarantees for real time services. As far as these two technical aspects are concerned, much research has been proposed in the last decade. First, with some trac models, a number of end to end delay calculation methods have been proposed [9, 10, 15, 16]. Also, many packet scheduling mechanisms have been provided [7, 11, 13, 17, 19, 20, 30] Finally admission control has been investigated as well [12, 14, 18] Much of this work addresses admission control and packet scheduling. Some deal with meeting end to end delay requirements. Some of the ....

....control systems: 1) NetEx [2, 3] has been selected as a generic connection oriented admission control with static priority system packet forwarding. This allows to study the e ect of connection based versus class based admission control with the same packet forwarding scheme (2) Virtual Clock [7, 9] has been selected in order to study whether there is any di erence in using a guaranteed rate scheduling policy such as Virtual Clock as opposed to a simple class based policy, such as class based static priority scheduling. In these experiments, we compare admission probability and run time ....

Norival R. Figueira, Joseph Pasquale, \An Upper Bound on Delay for the VirtualClock Service Discipline," IEEE/ACM Transactions on Networking, Vol. 3. Aug. 1995.

....route or excessive delay to the destination. Obviously, the per session performance bounds depend on the type of service discipline implemented at each switching node. Methodologies have been proposed to compute per session performance bounds under various service disciplines; 2] 3] and [5] [7] studied deterministic bounds, and [8] 9] and [11] derived probabilistic bounds. In this paper, we consider two distinctive service disciplines, rate proportional processor sharing (RPPS) 2] 15] and fixed rate processor sharing (FRPS) 3] 4] both of which can provide tighter per session ....

N. R. Figueira and J. Pasquale, "An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Trans. Networking, vol. 3, pp. 399--408, Aug. 1995.

....both buffer space requirements and the scheduler complexity. 68 It has been shown that if a flow s long term arrival rate is no greater than its reserved rate, a network of Virtual Clock servers can provide the same delay guarantee to the flow as a network of Weighted Fair Queueing (WFQ) servers [35, 47, 100]. In addition, it has been shown that a network of Jitter VC servers can provide the same delay guarantees as a network of Virtual Clock servers [28, 42] Therefore, a network of Jitter VC servers can provide the same guaranteed service as a network of WFQ servers. 5.3.2 Core Jitter VC (CJVC) In ....

N. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Transactions on Networking, 3(4):399,408, August 1995.

....scheme and show that under the scheme, coordinated schedulers can achieve the same end to end delay bound as WFQ. due to M M . 5.1. At Ingress Servers Suppose the ingress node services packets according to the virtual clock service discipline [10, 26]. Then the priority index increments at the ingress server are 1 K 3 K 8 c W (14) where, K = and is the reserved rate of flow . Conceptually, such virtually smoothing at the ingress node also spreads out the packets priority indexes at downstream ....

.... K L N P R R is the departure time of the # packet of flow from the virtual server with capacity , according to Definition 3 and Lemma 1, K W L (15) If # ) Q K ,D, Q K , then according to Theorem 2 in [10], K K W ( K , 16) where K is the departure time of the # packet of flow from the ingress server , W B D F W , W BED7F W , and ( K , is ....

[Article contains additional citation context not shown here]

N. Figueira and J. Pasquale. An upper bound on delay for the virtual clock service discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....control and packet scheduling, in terms of end to end delay guarantees for real time services. As far as these two technical aspects are concerned, much research has been proposed in the last decade. First, with some trac models, a number of end to end delay calculation methods have been proposed [13, 14, 19, 20] for a large variety of packet scheduling mechanisms [11, 15, 17, 21, 23, 24, 34] Finally admission control has been investigated as well [16, 18, 22] Much of this work addresses admission control and packet scheduling. Some of it deals with meeting end to end delay requirements. Some of the ....

Norival R. Figueira, Joseph Pasquale, \An Upper Bound on Delay for the VirtualClock Service Discipline," IEEE/ACM Transactions on Networking, Vol. 3. Aug. 1995.

....of end to end delay guarantees for real time services, our main interests are admission control and packet scheduling. As far as these two technical aspects are concerned, much research has been proposed. For a variety of traffic models, end to end delay calculation methods have been proposed [9, 10, 15, 16]. Also, many packet scheduling mechanisms have been provided [7, 11, 13, 17, 19, 20, Finally, admission control has been investigated as well [12, 14, 18] Some of the proposals have been implemented and deployed, for example, NetEx, RSVP, and Tenet. NetEx [2, 3] is a good working example of ....

....our class based approach, we ran a suite of simulation experiments to compare it with two forms of connection oriented admission control systems: 1) NetEx [2, 3] has been selected as a generic connection oriented admission control with static priority system packet forwarding. 2) Virtual Clock [7, 9] has been selected in order to study whether there is any difference in using a guaranteed rate scheduling policy such as Virtual Clock as opposed to a simple class based policy. Figure 3 shows the topology of the MCI ISP backbone network, which we use throughout the experiments. In the ....

Norival R. Figueira, Joseph Pasquale, "An Upper Bound on Delay for the Virtual Clock Service Discipline," IEEE/ACM Transactions on Networking, Vol. 3. Aug. 1995.

....as well as available traffic policing mechanisms for enforcement. We discuss the advantages and disadvantages of each traffic characterization method. Section 3. 2, where we describe the operations and implementations of a number of packet schedulers and review their available delay bound tests [31, 32, 33, 40, 52, 63, 74, 82, 102, 107, 110, 111, 112]. We describe the properties of each packet scheduling discipline, emphasizing tradeoffs between achievable network utilization and implementation overhead costs. 3.1 Traffic Characterization A traffic characterization should conform to a parameterized traffic model that can be enforced by some ....

....in equation (3.7) that F k i is set equal to the finishing time of the packet on connection i if packets are transmitted at fixed rate ae i . 3 The arriving packet is inserted into the sorted transmission queue according to F k i . Delay guarantees for VC schedulers were developed in [32, 107] for connections that conform to the (oe; ae) model. Two variants of the VC scheduling discipline are Burst Scheduling [63] and Leave inTime [33] In Burst Scheduling, traffic is not assumed to be a sequence of packet arrivals but rather a sequence of packet bursts. While VC assigns a virtual ....

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N. R. Figueira and J. Pasquale. An Upper Bound on Delay for the VirtualClock Service Discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....[18] takes scalability issues into account. As far as admission control and packet scheduling of end to end delay guarantees are concerned, much research has been proposed in the last decade. With some traffic models, a number of end to end delay calculation methods have been proposed [9, 10] for a large variety of packet scheduling mechanisms [7, 11, 14] Admission control has been investigated as well [12, 13] Much of this work addresses admission control and packet scheduling. Some of it deals with meeting end to end delay requirements. Some of the above proposals have been ....

Norival R. Figueira, Joseph Pasquale, "An Upper Bound on Delay for the Virtual Clock Service Discipline, " IEEE/ACM Transactions on Networking, Vol. 3. Aug. 1995.

....the variation is bounded too. Of particular interest here is Virtual Clock [21] This discipline is actually know to be equivalent to WFQ, under a suitable mapping between allocated bandwidths and shares. Virtual Clock provides no explicit control over delays or jitter. However, it has been shown [3] that under the assumption of leaky bucket constrained arrivals, VC provides bounded delays. The bounds are dependent on the allocated bandwidths. Since HFQ is a generalisation of WFQ, we expect similar results to apply to it. Other disciplines exist which decouple the delay bounds from the ....

Figueira, N.R. and Pasquale, J. An Upper Bound on Delay for the VirtualClock Service Discipline. IEEE/ACM Transactions on Networking 3, 4 (August 1995), 399-408.

....ned as the earliest due date (EDD) scheme where the due date of the nth cell of the ith VC is equal to the departure slot, F n i , of the cell from the ith RQ. Theorem 5 If P i2S i 1 then the RQDT (VirtualClock) scheme satis es the ( F n i F n i ) property. See Figueira and Pasquale [5] for a proof. Also, it is well known that (see e.g. page 42 of [6] under the RQDT scheme, the maximum service time experienced by a cell can be arbitrarily large. Even though the RQBT and RQDT schemes have similar properties, they are not identical: They produce di erent cell schedules. Consider ....

N. Figueira and J. Pasquale, \An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Transactions on Networking, vol. 3, no. 4, pp. 399-408, August 1995.

....research communities for the last decade or so. Many new packet scheduling algorithms (see, e.g. 7] 11] 16] 19] 20] and references therein) such as Virtual Clock (VC) and Weighted Fair Queueing (WFQ) have been proposed for the support of QoS guarantees. For example, it has been shown [8], 12] that in a network where WFQ schedulers (or VC schedulers) are employed at every router, end to end delay and bandwidth guarantees can be supported for each user traffic flow. Using these results as a reference model, the IETF has defined a guaranteed service [14] under its Integrated ....

.... rate based scheduling algorithms are employed at core routers (i.e. q = h) we have f j;k h Gamma a j;k 1 h L j;max r j h X i=1 Psi i h Gamma1 X i=1 i;i 1 : 31) This bound is analogous to those derived for fairqueueing latency rate server based scheduling algorithms [8], 12] 17] In particular, if Psi i = L ;max =C i , where L ;max is the maximum packet size permissible at the i th router and C i is its service capacity, then the above inequality yields precisely the same delay bound as is obtained for a flow in a network of Weighted Fair Queueing ....

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N. Figueira and J. Pasquale. An upper bound on delay for the virtual clock service discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....the earliest due date (EDD) scheme where the due date of the nth cell of the ith VC is equal to the departure slot, F n i , of the cell from the ith RQ. Theorem 5: If P i2S i 1 then the RQDT (VirtualClock) scheme satis es the ( F n i F n i ) property. See Figueira and Pasquale [6] for a proof. Also, it is well known that (see e.g. page 42 of [7] under the RQDT scheme, the maximum service time experienced by a cell can be arbitrarily large. Even though the RQBT and RQDT schemes have similar properties, they are not identical: They produce different cell schedules. ....

N. Figueira and J. Pasquale, \An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Transactions on Networking, vol. 3, no. 4, pp. 399-408, August 1995.

....of networking and telecommunication research communities for the last decade or so. Many new packet scheduling algorithms (see, e.g. 7, 14, 19, 24] such as Virtual Clock (VC) and Weighted Fair Queueing (WFQ) have been proposed for the support of QoS guarantees. For example, it has been shown [8, 15] that in a network where WFQ schedulers (or VC schedulers) are employed at every router, end to end delay and bandwidth guarantees can be supported for each user traffic flow. Using these results as a reference model, the Internet IETF has defined a guaranteed service [17] under its Integrated ....

.... rate based scheduling algorithms are employed at core routers (i.e. q = h) we have f j;k h Gamma a j;k 1 h L j;max r j h X i=1 Psi i h Gamma1 X i=1 i;i 1 : 29) This bound is analogous to those derived for fair queueing latency rate server based scheduling algorithms [8, 15, 20]. In particular, if Psi i = L ;max =C i , where L ;max is the maximum packet size permissible at the i th router and C i is its service capacity, then the above inequality yields precisely the same delay bound as is obtained for a flow in a network of Weighted Fair Queueing (WFQ) schedulers ....

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N. Figueira and J. Pasquale. An upper bound on delay for the Virtual Clock service discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....and as a consequence, reduce both buffer space requirements and the scheduler complexity. It has been shown that if a flow s long term arrival rate is no greater than its reserved rate, a network of Virtual Clock servers can provide the same delay guarantee to the flow as a network of WFQ servers [13, 16, 27]. In addition, it has been shown that a network of Jitter VC servers can provide the same delay guarantees as a network of Virtual Clock servers [9, 15] Therefore, a network of Jitter VC servers can provide the same guaranteed service as a network of WFQ servers. 3.2 Core Jitter VC (CJVC) In ....

N. Figueira and J. Pasquale. An upper bound on delay for the virtualclock service discipline. IEEE/ACM Transactions on Networking, 3(4), April 1995.

....S (or a cell schedule) is said to satisfy the nonnegative cell delay slackness property iff F n i (S) F n i 8n 1 and i 2 S (2) 5 That is, the delay experience by each cell is never greater than that experienced in the corresponding isolated single deterministic server queue. As shown in [4], under the condition X i2S 1 D i 1 (3) the VirtualClock scheme satisfies the nonnegative cell delay slackness property even when all the VCs are continuously backlogged. The HOL EDD scheme also satisfies this property. In fact, the HOL EDD scheme satisfies a stronger property called the ....

N. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....from the statistical multiplexer using the VirtualClock service scheduling scheme and define ffi n i = F n i Gamma F n i as the cell delay slackness of the nth cell of the ith VC. If P i2S OE i 1, then the VirtualClock scheme ensures that ffi n i 0 for all i 2 S and for all n 0 [4]. That is, the VirtualClock scheme ensures that all the cells depart from the statistical multiplexer at or before its due date. IEEE COMMUNICATIONS LETTERS 2 TABLE I The Minimum Cell Delay Slackness Implementation EVENT REACTION kth VC setup ffi k = 0, v k = 0 kth VC cell arrival place cell ....

N. Figueira and J. Pasquale, "An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Transactions on Networking, vol. 3, no. 4, pp. 399--408, August 1995.

....framework for traffic control. It could be used to provide performance guarantees by providing policing and guaranteed buffer space. No such results are presented in the paper, but an upper delay bound has been derived recently, and it is identical to that of the weighted fair queuing algorithm [5]. The method requires one virtual clock and a logical queue per flow. This may cause scaling problems when implemented. The clock increment must be computed per packet. 5.2 Weighted fair queuing (WFQ) This scheme [4, 16, 17] is akin to the previous one. Each arriving packet is stamped with the ....

N. Figueira and J. Pasquale, An Upper Bound on Delay for the Virtual Clock Service Discipline, IEEE/ACM Transactions on Networking, Vol. 3, No. 4, August 95, pp. 399-408.

....at the switch, namely its service deadline F n i . Head of queue cells are served according to the numerical order of their local time stamps. The bandwidth granularity of Virtual Clock is arbitrarily close to zero. Also, all Virtual Clock queues have a minimumbandwidth property parameter = 0 [3], 6] 14] There is also a non work conserving version of Virtual Clock [6] called Idling Virtual Clock) that attempts to better control cell delay jitter. V. Implementation Issues In general, when designing an ATM switch one should consider worst case per unit time complexity instead of ....

N.R. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Trans. Networking, Vol. 3, No. 4:pages 399--408, Aug. 1995.

....schedulers. Packetized generalized processor sharing is briefly discussed and a minimumbandwidth result for self clocked fair queueing is proved. We also prove a minimum bandwidth property for Virtual Clock; this result was independently obtained by Xie and Lam [14] and Figueira and Pasquale [6] as well. Finally, an idling Virtual Clock bandwidth scheduler is introduced and analyzed. In x5, we re examine our cut through assumption; in an elementary way, one can find a minimum bandwidth property for an non cut through implementation of a bandwidth scheduler given its minimum bandwidth ....

....using virtual time v(t) t (including Virtual Clock) were described and minimum bandwidth results were obtained. The results were obtained under both cut through and non cutthrough implementations. The minimum bandwidth property has been extended recently to tandem processor sharing nodes, see [6] for delay bounds of tandem nodes using Virtual Clock and [9] for a more general setting. That is, end to end delay bounds (and buffer sizing results) for arbitrary, tandem processor sharing nodes are obtained in terms of the delay through a reference FIFO buffer with devoted server. These results ....

N.R. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Trans. Networking, Vol. 3, No. 4:pages 399--408, Aug. 1995.

....bounds as WFQ with a simple timestamp computation algorithm, but the price paid is in terms of fairness. A backlogged session in the VirtualClock server can be starved for an arbitrary period of time as a result of excess bandwidth it received from the server when other sessions were idle [1, 17]. A scheduling algorithm that combines the delay and burstiness behavior of Weighted Fair Queueing, simple timestamp computations, and bounded unfairness, has so far remained elusive. The objective of our work is to develop an analytical framework for the design of such algorithms, ....

N. Figueira and J. Pasquale, "A upper bound on delay for the Virtualclock service discipline," IEEE/ACM Transactions on Networking, vol. 3, April 1995.

....VC is a much more efficient algorithm than PGPS, i.e. the computation of virtual clock values for VC scheduling is much simpler than the computation of virtual time finishing times for PGPS scheduling. The delay guarantee in (4) was independently discovered and proved by Figueira and Pasquale [4] and by us [12] We next discuss some of the differences between the two contributions. Firstly, one significant difference is our active flow definition, which is missing in [4] The condition for their delay guarantee is that sum of the reserved rates of all flows sharing the server does not ....

....times for PGPS scheduling. The delay guarantee in (4) was independently discovered and proved by Figueira and Pasquale [4] and by us [12] We next discuss some of the differences between the two contributions. Firstly, one significant difference is our active flow definition, which is missing in [4]. The condition for their delay guarantee is that sum of the reserved rates of all flows sharing the server does not exceed the server capacity [4] Theorem 1 herein requires that the reserved rates of only those flows that are active at time t be summed to determine whether or not the server ....

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Norival R. Figueira and Joseph Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Transactions on Networking, 3(4), August 1995.

....a SCFQ server, a sessions transmitting no faster than its reserved rate may still receive its worst case service. Another related discipline is the Virtual Clock algorithm [19] While Virtual Clock can provide the identical delay bound to a session whose source is constrained by a leaky bucket [5, 8, 15], its normalized Worst case Fair Index can be arbitrarily large even when there are only two sessions [13, 16] 5 Summary and Future Work We have made two contributions in this paper. First, we demonstrated that, contrary to popular belief, there can be a large discrepancy between the service ....

N. Figueira and J. Pasquale. An upper bound on delay for the virtualclock service discipline. IEEE/ACM Transactions on Networking, 3(4), April 1995.

....the ith RQ. An implementation of the VirtualClock scheme which neither uses cell stamping nor any monotonically increasing parameters is described in [8] Theorem 5 If P i2S OE i 1 then the RQDT (VirtualClock) scheme satisfies the ( F n i F n i ) property. See Figueira and Pasquale [3] for a proof. Also, it is well known that (see e.g. page 42 of [5] under the RQDT scheme, the maximum service time experienced by a cell can be arbitrarily large. Even though the RQBT and RQDT schemes have similar properties, they are not identical: They produce different cell schedules. ....

N. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

....at node j the variation of delay due to load fluctuation at the previous node j Gamma 1. It has been shown that if a flow s long term arrival rate is no greater than its reserved rate, a network of Virtual Clock servers can provide the same delay guarantee to the flow as a network of WFQ servers [8, 10, 18]. In addition, it has been shown that a network of Jitter VC servers can provide the same delay guarantees as a network of Virtual Clock servers [9] Therefore, a network of Jitter VC servers can provide the same guaranteed service as a network of WFQ servers. DRAFT 04 07 99 14:50 5 2.2 ....

N. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Transactions on Networking, 3(4), April 1995.

....we consider the design of packet schedulers appropriate for use in networks with a bounded delay service, that is, networks that provide deterministic (i.e. worst case) delay guarantees to all packets on a connection. Many packet schedulers have been considered for use in bounded delay services [7, 8, 13, 15, 29]. The well known Earliest Deadline First (EDF) scheduler has been studied in [7, 11, 12, 18] and is distinguished in that it has optimal efficiency : for a given set of connections, EDF can support delay guarantees that are at least as tight as those provided by any other packet scheduler [11, ....

N. R. Figueira and J. Pasquale. An Upper Bound on Delay for the VirtualClock Service Discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

.... bounds at each switch independently and use the sum of these local delay bounds as the end to end delay bound [16] Alternatively, smaller end to end delay bounds can be obtained by taking into account the dependencies in the sucessive switches that a connection traverses [47] 10] 68] 19] [17], 23] For the first type of solution, in order to derive local delay bound, traffic needs to be characterized on a per connection basis at each switch inside the network. For the second type of solution, while the end to end delay bound may be derived for Virtual Clock, WFQ, SCFQ based only on ....

....to derive local delay bound, traffic needs to be characterized on a per connection basis at each switch inside the network. For the second type of solution, while the end to end delay bound may be derived for Virtual Clock, WFQ, SCFQ based only on the source traffic characterization [47] 10] [17], 23] as will be shown in Section III G, the delay bound couples with bandwidth allocation. In [47] such a source allocation strategy is called rate proportional allocation. It has been shown more general resource allocation strategies that decouples throughtput and delay bounds can result in ....

N. Figueira and J. Pasquale. An upper bound on delay for the virtualclock service discipline, December 1994. To appear in IEEE/ACM Transactions on Networking.

.... Gamma1 ; 8i 1 where d i is the departure time of the i th cell arriving to FIFO n (OE : ae=c is the bandwidth partitioning parameter of FIFO n) Minimum bandwidth properties have been proved for several bandwidth schedulers: PGPS (WFQ) with parameter = 0 [6] Virtual Clock 1 with = 0 [2, 3, 7], self clocked fair queueing (SCFQ) with parameter N Gamma 2 [3] and IVC with parameter N Gamma 1 [3] Also, round robin type schedulers clearly have a minimum bandwidth property with on the order of the frame size. 3 General End to End Delay Bounds and Buffer Sizing Results We now consider ....

....uses a FIFO with bandwidth requirement ae cells s at each hop. Let Pi h be the propagation delay from the UNI device to node h. Finally, let fF i g be the VC VFTs based on arrivals fa i g and bandwidth requirement ae cell s. 3. 1 A General End to End Delay Bound Our end to end delay bound (see [2, 7] for the Virtual Clock case and [6, 5] for PGPS) is proved using the following two lemmas each of which is the result of an elementary inductive argument. 1 Actually, in [3] it was shown that Virtual Clock under a cut through implementation has minimumbandwidth parameter = Gamma1. Lemma 1: ....

N.R. Figueira and J. Pasquale. An upper bound on delay for the VirtualClock service discipline. IEEE/ACM Trans. Networking, Vol. 3, No. 4:pages 399--408, Aug. 1995.

No context found.

Figueira, N., and Pasquale, J. An upper bound on the delay for the virtual clock service discipline. 1995).

....is by permission of the Association for Computing Machinery, Inc. ACM) To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specihc permission and or a fee. SIGCOMM 95 Cambridge, MA USA 1995 ACM 0 89791 711 1 95 0008. 3. 50 207 recently proven in [7]) Jitter EDD, RCSP, and Stop and Go also provide an upper bound on delay jitter. Providing an upper bound on delay has been a major point of concern for previously proposed service disciplines; however, even this is not enough. The delay distribution of packets is likely to be very useful for ....

.... Wz, s is the finishing transmission time of packet i in the reference server (i.e. the time ref the last bit of packet i leaves the reference server) and Di, s is the delay of packet i in the reference server, i.e. D ref Wt, Wt, s is related to t, s and Lt, s by the following equation (proof in [7]) W = max t,s, W , ls L s,i l, 1) where W0, s = tl, s The Leave in Time Service Discipline We present the Leave in Time service discipline as a constmction in three steps: a base server algorithm based on the reference server, and two generalizations that result in the final version. Base ....

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N.R. Figueira and Joseph Pasquale, "An Upper Bound on Delay for the VirtualClock Service Discipline," 1EEE/ACM Transactions on Networking, Vol. 3, No. 4, August 1995, (in press).

.... and sink devices [48] Leave in Time, a new packet switching service discipline that provides distributional end toend performance (e.g. delay) bounds [50] building on new results for performance bounds of other service disciplines that were unknown, and in some cases, believed to not exist [51] 38 . Software implementation techniques for improving throughput and latency in TCP IP, based on one of the most detailed studies of where time is spent in a commonly used TCP IP implementation [83] The Multimedia Multicast Channel (MMC) a group communication abstraction unique for its ....

N. Figueira and J. Pasquale, "An upper bound on delay for the VirtualClock service discipline, " IEEE/ACM Transactions on Networking, 3(4), August 95, pp. 399-408.

....(this includes VirtualClock for which an upper bound on endThis work was supported in part by a scholarship from CAPES and UFRJ (Brazil) and by grants from NASA and NSF. Technical Report CS95 426, University of California, San Diego, May 1995. 2 to end delay was unknown until recently proven in [7]) Jitter EDD, RCSP, and Stop and Go also provide an upper bound on delay jitter. Providing an upper bound on delay has been a major point of concern for previously proposed service disciplines; however, even this is not enough. The delay distribution of packets is likely to be very useful for ....

....of packet i in the reference server (i.e. the time the last bit of packet i leaves the reference server) and is the delay of packet i in the reference server, i.e. Queue Received Packets r s t i s , L i s , W i s , D i s , ref 4 . is related to and by the following equation (proof in [7]) i 1, 1) where . 2.2 The Leave in Time Service Discipline We present the Leave in Time service discipline as a construction in three steps: a base server algorithm based on the reference server, and two generalizations that result in the final version. Base Algorithm: Consider a service ....

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N. R. Figueira and Joseph Pasquale, "An Upper Bound on Delay for the VirtualClock Service Discipline," IEEE/ ACM Transactions on Networking, Vol. 3, No. 4, August 1995, (in press).

....(Brazil) and by grants from NASA and NSF. Technical Report CS95 432, University of California, San Diego, July 1995. This document was created with FrameMaker 4.0. 4 Page 2 [4, 5] All of these service disciplines provide an upper bound on end to end delay (including VirtualClock, as proven in [3]) which has been one of their major points of concern. In general, one cannot describe a packet switching rate based server that can support multiple simultaneous sessions as providing each session a constant service rate. This is because, for a rate based server with capacity C, a session will ....

....by a LBR(r, service discipline. J Time J J 0 J D i ref h L i ( D i D i ref h L i ( D i ref h L i ( L i C Page 5 , 5) which guarantees that for any kind of session (which we prove next) Lemma 1: If , then . Proof of Lemma 1: This proof uses the following result from [3] which calculates the finishing transmission time of packets of a session in its reference server: 6) i 1. 7) From (6) and (7) we have that , i 1, which implies that . Hence . o Note that if (5) is not true for a service discipline (i.e. if ) it is possible for packet i to be ....

[Article contains additional citation context not shown here]

N. R. Figueira and Joseph Pasquale, "An Upper Bound on Delay for the VirtualClock Service Discipline," IEEE/ ACM Transactions on Networking, Vol. 3, No. 4, August 1995, (in press).

....where F is the actual finishing transmission time of the packet, F is the deadline of the packet, ffi 0, and ffi is a constant. Thus, by schedulable we simply mean 0 schedulable. Schedulability determination generally involves intricate and long proofs (e.g. Delay EDD [1] and VirtualClock [2]) In this paper we show that, no matter how one assigns deadlines, there is a simple schedulability condition for deadline ordered servers. This schedulability condition is necessary and sufficient for preemptive deadlineordered scheduling. For non preemptive deadline scheduling, it is only ....

....schedulability condition of some well known service disciplines such as VirtualClock, PGPS, Stop and Go, and Delay EDD. We also discuss the applicability of our results to preemptive servers in the analysis of scheduling algorithms for multiprogramming in a real time environment. VirtualClock In [2], it was proved that VirtualClock [14] is able to provide an upper bound on delay for some types of sessions if X s2 Omega r s C, 31) where C is the capacity of the outgoing link of the server, r s is the reserved rate of session s (the reserved rate of a non real time session is equal to ....

[Article contains additional citation context not shown here]

N. R. Figueira and J. Pasquale, "An Upper Bound on Delay for the VirtualClock Service Discipline," In IEEE/ACM Transactions on Networking, Vol. 3, No. 4, pp. 399-408, August 1995.

.... [26] VirtualClock [ 29] PGPS [17, 18, 19, 20] Stop and Go [9, 10, 11] and Hierarchical Round Robin [13] All of these service disciplines provide an upper bound on end to end delay (this includes VirtualClock for which an upper bound on end to end delay was unknown until recently proven in [7]) Jitter EDD, RCSP, and Stop and Go also provide an upper bound on delay jitter. Providing an upper bound on delay has been a major point of concern for previously proposed service disciplines; however, even this is not enough. The delay distribution of packets is likely to be very useful for ....

.... is the length of packet i of the session, is the finishing transmission time of packet i in the reference server (i.e. the time the last bit of packet i leaves the reference server) and is the delay of packet i in the reference server, i.e. is related to and by the following equation (proof in [7]) i 1, 1) where . Queue Received Packets r s t i s , L i s , W i s , D i s , ref D i s , ref W i s , t i s , W i s , t i s , L i s , W i s , max t i s , W i 1 s , L i s , r s = W 0 s , t 1 s , The Leave in Time Service Discipline We ....

[Article contains additional citation context not shown here]

N. R. Figueira and Joseph Pasquale, "An Upper Bound on Delay for the VirtualClock Service Discipline," IEEE/ACM Transactions on Networking, Vol. 3, No. 4, August 1995, (in press).

No context found.

Norival R. Figueira and Joseph Pasquale, "An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Transactions on Networking, vol. 3, no. 4, pp. 399--408, 1995.

No context found.

Norival R. Figueira and Joseph Pasquale, "An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Transactions on Networking, vol. 3, no. 4, pp. 399--408, 1995.

No context found.

N. Figueira and J. Pasquale. An upper bound on delay for the virtual clock service discipline. IEEE/ACM Transactions on Networking, 3(4):399--408, August 1995.

No context found.

N. Figueira and J. Pasquale, "An upper bound on delay for the VirtualClock service discipline," IEEE/ACM Trans. Networking Vol. 3, No. 4, pp. pages 399--408, Aug. 1995.

No context found.

N. R. Figueira and J. Pasquale. An upper bound on delay for the virtual clock service discipline. IEEE/ACM Trans. Networking, vol. 3, no. 4, 1995.

No context found.

N. R. Figueira and J. Pasquale. An upper bound on delay for the virtual clock service discipline. IEEE/ACM Trans. Networking, vol. 3, no. 4, 1995.

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