R. L. Cruz, "Service burstiness and dynamic burstiness measures: A framework," J. High Speed Networks, vol. 1, no. 2, pp. 105--127, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....algorithms can be used to bound delay in subnetworks. For example, in [3, 4] algorithms are designed to bound packet delays in an FDDI network. It should be noted that most of the current delay bounding solutions assume a simple network model where link delays between switches are constant [20, 21, 51, 66, 68, 38, 6]. Constant delay links have the desirable property that the traffic pattern at the receiving end of the link is the same as that at the transmitting end of the link. This property is important for these solutions because they use the characterization of the output traffic from a scheduler as the ....

....to establish that holding in the rate controllers will not increase the end to end delay bound. ffl The theorem assumes links with bounded, but possibly variable, delay. Most of the existing solutions proposed to bound end to end delay in a networking environment assume links with constant delay [20, 21, 51, 66, 68, 38, 6]. Constant delay links have the nice property that the traffic pattern at the receiving end of the link is the same as that at the transmitting end of the link. This property is important for existing bounding solutions because central to their analysis is the technique of characterizing output ....

Rene L. Cruz. Service burstiness and dynamic burstiness measures: A framework. Journal of High Speed Networks, 1(2), 1992. 117

....flow that goes through such a switch fabric. Interested readers are referred to [24] for a complete analysis. In our analysis we use the notion of Worst Case Fairness Index (WFI) that represents the maximum time before serving two packets of a given flow [12] We also use the theory presented in [13] and the notion of the Service Burstiness Index (SBI) Assume that a flow is leaky bucket shaped with burstiness parameters rtsuDgvHsp . We state without proof the following Theorem: Theorem 1: The total delay of a packet of flow in the entire switch is upper bounded by r sS xw sy ....

R.L. Cruz, "Service burstiness and dynamic burstiness measures: A framework, " Journal of High Speed Networks, vol. 1, no. 2, pp. 105--127, 1992.

....end to end delay and cell loss rate. These requirements must be satisfied at extremely high speeds without compromising on network utilization. To provide for QoS guarantees in packet switched networks, a number of service disciplines have been proposed, including [8] 24] 9] 10] 26] 5] [6], 25] 19] 18] 11] 12] 7] Many of these service disciplines are based on a prioritization of the network resources to match different QoS requirements. In these schemes, packets are assigned priority values and are transmitted in a highest priority first order . To implement this ....

R. L. Cruz, "Service burstiness and dynamic burstiness measures: a framework", Journal of High Speed Networks, vol. 1, no. 2, pp. 105-127, 1992.

....the bandwidth properties of the flow. Under PFQ it is not possible to differentiate between two flows that have the same bandwidth requirements but different delay constraints without over reservation. A number of solutions to this drawback have been developed using the Service Curve approach of [Cruz92, Cruz95] such as Service Curve Earliest Deadline (SCED) Sariowan95] and the Fair Service Curve (FSC) Stoica97] The Service Curve approach allows a separation of a flow s delay and bandwidth requirements, assigning service curves of different shapes to different flows convex curves for ....

R. Cruz. Service burstiness and dynamic burstiness measures: A framework . Journal of High Speed Networks, 1(2):105--127, 1992. (p 52)

....4.2. Combining DFS with Fair Airport Scheduling We draw upon the concept of fair airport scheduling to enhance DFS with an auxiliary policy to allocate idle bandwidth to ineligible runnable tasks. The notion of fair airport was proposed in the context of scheduling packets at a network router [8, 12]. A fair airport scheduler attempts to combine a potentially non work conserving scheduling algorithm with an auxiliary scheduler to ensure rate regulator Guaranteed service queue Auxiliary service queue GSQ scheduler ASQ scheduler FA Server Figure 3. Fair Airport Scheduling Algorithm ....

....GSQ becomes empty. Different scheduling algorithms may be employed for servicing packets in the guaranteed service and auxiliary service queues. Depending on the exact choice of the ASQ and GSQ schedulers, it is possible to theoretically prove properties of the combined scheduling algorithm (see [8, 12] for examples) The concept of fair airport scheduling can also be employed to schedule tasks in a multiprocessor system. Our instantiation of fair airport, referred to as DFS FA, employs DFS as the GSQ scheduler. The rate regulator for each task is simply its eligibility criterion (Eq 6) the ....

R. Cruz. Service Burstiness and Dynamic Burstiness Measures: A Framework. Journal of High Speed Networks, 2:105--127, 1992.

....DFS with Fair Airport Scheduling Algorithms We draw upon the concept of fair airport scheduling to enhance DFS with an auxiliary policy to allocate idle bandwidth to ineligible runnable tasks. The notion of fair airport was proposed in the context of scheduling packets at a network router [10, 14]. A fair airport scheduler attempts to combine a potentially non work conserving scheduling algorithm with an auxiliary scheduler to ensure work conserving behavior at all times. Each packet (or task) in a fair airport scheduler joins a rate regulator and an Auxiliary Service Queue (ASQ) see ....

....GSQ becomes empty. Different scheduling algorithms may be employed for servicing packets in the guaranteed service and auxiliary service queues. Depending on the exact choice of the ASQ and GSQ schedulers, it is possible to theoretically prove properties of the combined scheduling algorithm (see [10, 14] for examples) The concept of fair airport scheduling can also be employed to schedule tasks in a multiprocessor system. Our instantiation of fair airport, referred to as DFS FA, employs DFS as the GSQ scheduler. The rate regulator for each task is simply its eligibility criterion (Eq 6) the ....

R.L. Cruz. Service Burstiness and Dynamic Burstiness Measures: A Framework. Journal of High Speed Networks, 2:105-- 127, 1992.

....of SFQ servers presented in Section 2 6 . 6 We would like to warn the reader of a potential pitfall. It is possible that some may reach the conclusion that this analysis would hold even if the throughput of a server was modeled by a Service Burstiness server which is similar to a FC server [3]. However, even though the throughput guaranteed to a flow by a Virtual Clock server conforms to Service Burstiness, it can be shown that Virtual Clock when used for hierarchical link sharing provides no guarantees. 17 Hierarchical SFQ scheduler not only achieves the objectives of hierarchical ....

R.L. Cruz. Service Burstiness and Dynamic Burstiness Measures: A Framework. Journal of High Speed Networks, 2:105--127, 1992.

....flow that goes through such a switch fabric. Interested readers are referred to [24] for a complete analysis. In our analysis we use the notion of Worst Case Fairness Index (WFI) that represents the maximum time before serving two packets of a given flow [12] We also use the theory presented in [13] and the notion of the Service Burstiness Index (SBI) Assume that a flow n is leaky bucket shaped with burstiness parameters (oe n ; r n ) Also let r (i;j) P n2F (i;j) r n , where F (i;j) is the set of flows between (i; j) We state without proof the following Theorem: Theorem 1: The total ....

R.L. Cruz, "Service burstiness and dynamic burstiness measures: A framework, " Journal of High Speed Networks, vol. 1, no. 2, pp. 105--127, 1992.

....; t 2 ) W (i;j) t 1 ; t 2 ) for such an interval. Let Wn (t 1 ; t 2 ) denote the amount of packettraffic of flow n served by S (i;j) and hence by the switch scheduler) during [t 1 ; t 2 ] In deriving the worst case delay bounds, some of the definitions and analysis techniques used by Cruz in [13] and Bennett Zhang in [12] have been very useful to us. For completeness, we state two definitions from [12] Definition 1: A server node s is said to guarantee a Worstcase Fair Index (WFI) of ff m to flow m, offering a service share of rm rs to the flow, if for any interval [t 1 ; t 2 ] for ....

....connected in tandem, guarantees a delay bound of oe m fl (1) m fl (2) m Lm;max rm to flow m, where Lm;max is the maximum length of a packet of flow m. The proof of Lemma 1 is in Appendix B. The above result can also be easily extended to a network of k servers connected in tandem (see [13] for a similar result; 12] also states the result for the special case of single server) Now, using Lemma 1 and Theorem 1 we can bound the total delay seen by packets of flow n in the system shown in Figure 5. Corollary 1: The total delay of a packet of flow n in the entire switch is ....

R.L. Cruz, "Service burstiness and dynamic burstiness measures: A framework, " Journal of High Speed Networks, vol. 1, no. 2, pp. 105--127, 1992.

....with 160 byte packets. To achieve a worst case delay of 5 ms, according to Eq. 3) one should reserve 2 256 Kbps, which is four times more than the flow s bandwidth requirements 2. 2 Service Curve Model To address this problem, Cruz has proposed a new service model, called service curve (SC) [2, 3], in the context of real time guaranteed traffic. In this model, each flow is associated with a service curve S i , which is a continuous non decreasing function. A flow i is said to be guaranteed a service curve S i ( Delta) if for any time t 2 when the flow is backlogged, there exists a time t ....

R.L. Cruz. Service burstiness and dynamic burstiness measures: A framework. Journal of High Speed Networks, 1(2):105--127, 1992.

....[6] These schemes differ from each other in the strategies they employ to enforce rate control and in the policy they use to service packets. More recent schemes seek to maintain a high level of fairness while reducing the complexity of emulating General Processor Sharing (GPS) scheduling policy [4, 1, 3]. Very few of these schemes, however, address the question of how to assign per node delay values, or equivalently service rates, to a new session to meet its end to end delay requirements. An approach, proposed by Parekh [5] computes the largest and smallest values of OE that would ensure the ....

R. L. Cruz. Service Burstiness and Dynamic Burstiness Measures: A Framework . Journal of High Speed Networks, 2:105--127, 1992.

....with 160 byte packets. To achieve a worst case delay of 5 ms, according to Eq. 1) one should reserve 2 256 Kbps, which is four times more than the flow s bandwidth requirement 2. 2 Service Curve Model To address this problem, Cruz has proposed a new service model, called service curve (SC) [10, 11], in the context of real time guaranteed traffic. In this model, each flow is associated with a service curve S i ( Delta) which is a continuous non decreasing function. A flow i is said to be guaranteed a service curve S i ( Delta) if for any time t 2 when the flow is backlogged, there exists a ....

R.L. Cruz, "Service burstiness and dynamic burstiness measures: A framework," Journal of High Speed Networks, vol. 1, no. 2, pp. 105-- 127, 1992.

....6, and evaluate its performance based on both simulation and measurement experiments in Section 7. We discuss related work in Section 8 and conclude the paper in Section 9. 3 2 Background: Service Curve Based QoS As discussed in Section 1, we use the service curve abstraction proposed by Cruz [5, 6] as the building block to define the idealized link sharing model. A session i is said to be guaranteed a service curve S i ( Delta) where S i ( Delta) is a non decreasing function, if for any time t 2 when session i is backlogged, there exists a time t 1 t 2 , which is the beginning of one of ....

R.L. Cruz. Service burstiness and dynamic burstiness measures: A framework. Journal of High Speed Networks, 1(2):105--127, 1992.

....A packet on arrival joins the rate controller for its flow. The rate controller delays packets to ensure that the output traffic from the flow conforms to specified constraints. Once a packet passes through the rate controller, it joins a queue that we refer to as Guaranteed Service Queue (GSQ) [7]. Packets are serviced from GSQ using a work conserving GSQ scheduling algorithm. Observe that the rate controller limits the service received by a flow from the GSQ in any time interval. Hence, intuitively, the difference in service received by any two flows in any time interval from the GSQ is ....

....have been introduced in the literature. A comparison of various definitions and justifications for the appropriateness of this definition is presented in [12] 6 The class of Fair Airport scheduling algorithms derives its name from the class of Airport scheduling algorithms presented in [7]. 2 Server Guaranteed Service Queue GSQ Rate Controller Figure 1: Non work conserving RCSD Server Server Guaranteed Service Queue GSQ Auxilary Service Queue Server Rate Controller SFQ Figure 2: Fair Airport Scheduling Algorithms the service received from GSQ is fair (we will demonstrate this ....

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R.L. Cruz. Service Burstiness and Dynamic Burstiness Measures: A Framework. Journal of High Speed Networks, 2:105--127, 1992. 15

....Therefore, it is very important for the algorithm to require a small number of operations per packet. ffl The basic mechanism and parameters used by the algorithm to make scheduling decisions. Of specific interest is whether the algorithm supports separate delay and rate guarantees, e.g. [11, 24, 62], or combines the two e.g. 29, 46, 58] Separate rate and delay guarantees allow greater flexibility. ffl The flexibility of the algorithm in handling traffic in excess of the amount for which the service guarantees have been requested. Some algorithms easily handle excess traffic while others ....

....by how it deviates from the behavior of this perfect fluid server. The error terms C and D of the Guaranteed Service are used to capture those deviations (see [47, 54] for details) The behavior of a Guaranteed Services scheduler can be accurately described using the notion of service curves [11, 12]. Analogous to the way a traffic envelope bounds the amount of input traffic, a service curve can be used to provide a lower bound on the amount of service received by a flow at an individual network element (see [12, 43, 53] for definitions of service curves) The Guaranteed Services scheduler ....

R. L. Cruz. Service burstiness and dynamic burstiness measures: A framework. J. High Speed Networks, 1(2):105--127, 1992. 14

....end to end delay and cell loss rate. These requirements must be satisfied at extremely high speeds without compromising on network utilization. To provide for QoS guarantees in packet switched networks, a number of service disciplines have been proposed, including [8] 24] 9] 10] 26] 5] [6], 25] 19] 18] 11] 12] 7] Many of these service disciplines are based on a prioritization of the network resources to match different QoS requirements. In these schemes, packets are assigned priority values and are transmitted in a highest priority first order 1 . To implement this ....

....is smaller than B[3] value which is 10, there is no swap. The value 4 is moved down to T [3] value and the left branch is taken. T [3] operation is set to enq. No new operation starts at this stage. Cycle 5: f(3) is executed by the operation enqueue(4) Figure 15 (e) It finds an inactive node, B[6], and writes the value 4 into it, thus ending this enqueue operation. Since there is no local enqueue necessary at level L 4 , T [4] operation is set to nop. At the same time, the dequeue operation starts working on 1 with the procedure localdequeue (1) called by f(1) The highest value, 16, is ....

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R. L. Cruz, "Service burstiness and dynamic burstiness measures: a framework", Journal of High Speed Networks, vol. 1, no. 2, pp. 105-127, 1992.

....A key factor in obtaining these smaller delay bounds is the ability to take into account (delay) dependencies in the successive nodes that a connection has to cross, which is in general very difficult to do with other policies. One notable attempt at addressing this general problem is that of [6] which introduced the concept of service An earlier version of this paper was presented at the IEEE Infocom 96 Conference. The paper was selected by the conference as one of its top papers and referred to the Transactions for possible publication after the Transactions own independent review L. ....

....NY 10598, USA. K. N. Sivarajan is with the ECE Department, Indian Institute of Science, Bangalore 560012, India. burstiness, and used it to provide a framework to characterize service disciplines and evaluate their end to end delay performance. However, the generality of the framework in [6] did not result in as tight end to end delay bounds as those obtained by focusing on a specific policy. For example, the bounds available based on the techniques of [6] are no better than the looser bounds found in [12] In this paper we concentrate on Rate Controlled Service (RCS) disciplines, ....

[Article contains additional citation context not shown here]

R. L. Cruz. Service burstiness and dynamic burstiness measures: A framework. Journal of High Speed Networks, 1(2):105--127, 1992.

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R. L. Cruz. Service burstiness and dynamic burstiness measures: a framework. Journal of High Speed Networks, vol. 1, no. 2, 1992, pp. 105127.

.... t 0, there exists s t such that R out (t) Gamma R in (s) S(t Gamma s) Definition 1 has been previously reported in [17] It has also been independently made by Agrawal and Rajan [1] and Le Boudec [14] Earlier related definitions of service guarantees were made independently by Cruz [7], Hung and Kesidis [13] and Stiliadis and Varma [18] Given two functions F and G defined on the nonnegative integers, define the convolution of F and G, written F G, as F G(x) min x1 x2=x;x1;x20 fF (x 1 ) G(x 2 )g : The convolution operator is analogous to conventional convolution ....

R. L. Cruz, "Service burstiness and dynamic burstiness measures: a framework," Journal of High Speed Networks, vol. 1, no. 2, pp. 105-127, 1992.

.... or priority scheduler) Service curves, with a somewhat different definition than in this paper, were introduced by Parekh and Gallager [21, 22] to study generalized processor sharing (GPS) The idea of using a service curve as a general characterization of a scheduling policy was proposed by Cruz [7], and refined in [8] Closely related service definitions, which are a special case of the service curve framework in this paper, were made by Stiliades and Varma [26] Hung and Kesidis [16] and Goyal, Lam, and Vin [15] These three latter definitions are essentially equivalent, and have recently ....

R. L. Cruz. Service burstiness and dynamic burstiness measures: a framework. Journal of High Speed Networks, vol. 1, no. 2, pp. 105-127, 1992.

....Roughly speaking, if a packet suffers the worst possible delay at one network element, the packet will not suffer the worst possible delay at the next hop. Parekh and Gallager [14] 15] present results which make use of this idea; more recent work has extended these results in other directions [6] [8] 16] The aim of this paper is to review some of these results in a reasonably self contained and unified way. We will make heavy use of the concept of a service curve, which has its roots in the work of Parekh and Gallager [14] 15] As we will see, a service curve partially characterizes ....

R. L. Cruz. Service burstiness and dynamic burstiness measures: a framework. Journal of High Speed Networks, vol. 1, no. 2, 1992, pp 105-1127.

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R. L. Cruz, "Service burstiness and dynamic burstiness measures: A framework," J. High Speed Networks, vol. 1, no. 2, pp. 105--127, 1992.

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R. L. Cruz. Service burstiness and dynamic burstiness measures: A framework. Journal of High Speed Networks,1(2' 1992

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R. L. Cruz, "Service burstiness and dynamic burstiness measures: A framework", J. High Speed Networks, vol. 1, no.2, pp.105-127, 1992.

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R. L. Cruz, "Service burstiness and dynamic burstiness measures: A framework," J. High Speed Networks, vol. 1, no.2, 1992.

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