We define a class of Guaranteed Rate (GR) scheduling algorithms. The GR class includes Virtual Clock, Packet-by-Packet Generalized Processor Sharing and Self Clocked Fair Queuing. For networks that employ scheduling algorithms belonging to GR, we present a method for determining an upper bound on end-to-end delay. The method facilitates determination of end-to-end delay bounds for a variety of sources. We illustrate the method by determining end-to-end delay bounds for sources conforming to Leaky Bucket and Exponentially Bounded Burstiness.

In this paper, we develop bounds on the individual session backlog and delay distribution under the Generalized Processor Sharing (GPS) scheduling discipline . This work is motivated by, and is an extension of, Parekh and Gallager 's deterministic study of the GPS scheduling discipline with leaky-bucket token controlled sessions [15], [16]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in [18] as a source traffic characterization, we establish results that extend the deterministic study of GPS: for a single GPS server in isolation, we present statistical bounds on the distributions of backlog and delay for each session. In the network setting, we show that networks belonging to a broad class of GPS assignments, the socalled Consistent Relative Session Treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the distribution of backlog and delay for each session in a Rate Proportional Processor Sharin...

In this paper, we define a class of generalized Guaranteed Rate (GR) scheduling algorithms that includes algorithms which allocate variable rate to packets of a flow. We define work-conserving generalized Virtual Clock, Packet-by-Packet Generalized Processor Sharing, and Self-Clocked Fair Queuing scheduling algorithms that can allocate variable rate to the packets of a flow. We also define scheduling algorithms suitable for servers where packet fragmentation may occur. We demonstrate that if a class of rate controllers is employed for a flow in conjunction with any scheduling algorithm in GR, then the resulting non-work-conserving algorithm also belongs to GR. This leads to the definition of several non-work-conserving algorithms. We then present a method for deriving the delay guarantee of a network of servers when: 1) different rates are allocated to packets of a flow at different servers along the path and the bottleneck server for each packet may be different, and 2) packet fragmentation and/or reassembly may occur. This delay guarantee enables a network to provide various service guarantees to flows conforming to any specification. We illustrate this by utilizing delay guarantee to derive delay bounds for flows conforming to Leaky Bucket, Exponentially Bounded Burstiness, and Flow Specification. Our method for determining these bounds is valid in internetworks and leads to tighter results.

We consider large buffer asymptotics for feed-forward networks of discrete-time queues with deterministic service rate shared by multiple classes of streams subject to work conserving service policies. First we review the concept of effective bandwidths for traffic streams sharing a common buffer subject to subject to tail constraints on the workload distribution. Next, we obtain the effective bandwidth of the departure process from such a queue, proving that in fact the effective bandwidth of the output is at worst equal to that of the input, and depending on the service rate, strictly less than that of the input. We then define the notion of a decoupling bandwidth and the associated constraints, guaranteeing that asymptotics within the network are decoupled. These results provide a framework for call admission schemes which are sensitive to constraints on the tail distribution of the workload or approximate cell loss probabilities. Our results require relatively weak assumptions on both the traffic streams and service policies. We consider the problem of “optimal ” traffic shaping (via buffering) subject to a loss constraint. Finally, we discuss our results in the context of resource management for ATM networks. 1

Generalized Processor Sharing (GPS) is the basis for the packet scheduler of choice in IP routers and ATM switches of the future. The currently accepted approach for the design of GPS schedulers is based on deterministic QoS guarantees, which, it is generally accepted, is overly conservative and leads to limitations on capacity. To address this problem we develop a framework for GPS scheduling which is based on statistical QoS guarantees and statistical multiplexing. We give the design of GPS weights which maximize the coverage of operating points, and also the design of the connection admission control (CAC). The general framework is end-to-end, with two heterogeneous QoS classes coexisting with a third, best effort class. Each QoS class has a specified delay bound together with a bound on the probability of its violation. An important objective is to maximize the bandwidth available to best effort traffic while just satisfying the guarantees of the QoS classes. To this end, we consid...

We develop a network calculus for processes whose burstiness is stochastically bounded by general decreasing functions. This calculus enables us to prove the stability of feedforward networks and obtain statistical upper bounds on interesting performance measures such as delay, at each buffer in the network. Our bounding methodology is useful for a large class of input processes, including important processes exhibiting "subexponentially bounded burstiness" such as fractional Brownian motion. Moreover, it generalizes previous approaches and provides much better bounds for common models of real-time traffic, like Markov modulated processes and other multiple time-scale processes. We expect that this new calculus will be of particular interest in the implementation of services providing statistical guarantees.

We prove asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with only two queues needs special attention, as under this case, it is shown that the upper bounds and lower bounds match, thus yielding exact bounds. This result is established in this part (Part I) of the paper. The general case is much more complicated, and is treated separately in Part II of the paper [42], where tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of GPS scheduling. The proofs use sample-path large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for high-speed communication networks. 1 Int...

Provision of Quality-of-Service (QoS) guarantees is an important and challenging problem in the design of integrated-services packet networks. Call admission control is an integral part of the challenge and is closely related to other aspects of networks such as service models, scheduling disciplines, traffic characterization and QoS specification. In this paper we provide a theoretical framework within which call admission control schemes with multiple statistical QoS guarantees can be constructed for the Generalized Processor Sharing (GPS) scheduling discipline (also known as Weighted Fair Queueing). Using this framework, we present several admission control schemes for both session-based and class-based service models. The theoretical framework is based on recent results in statistical analyses of the GPS scheduling discipline and the theory of effective bandwidths. Both optimal schemes and suboptimal schemes requiring less computational effort are studied under these service models...

Abstract — Generalized Processor Sharing (GPS) has gained much popularity in recent years as a simple and effective scheduling mechanism for the provisioning of Quality of Service (QoS) in emerging high-speed networks. For supporting deterministic end-to-end delay guarantees, GPS is known to be sub-optimal in comparison to the Earliest Deadline First (EDF) scheduling discipline; nevertheless it is often prefered over EDF due to its simplicity. In this paper, using analytical frameworks developed recently in the literature, we reassess the merits of GPS as compared to EDF in the setting of statistical delay service. Our contributions are threefold. The statistical frameworks in the literature enable the aggregate losses (i.e., delay bound violations) at an EDF scheduler to be estimated – our first contribution, therefore, is to develop a mechanism that allows the aggregate losses to translate to per-flow guarantees. This is achieved by means of a simple packet discard scheme that drops packets fairly when delay violations are imminent at the EDF scheduler. The discard mechanism has a constant complexity and is feasible for implementation in current packet switches. The ability to derive the per-flow guarantees from the agregate allows a direct comparison between EDF and GPS – our next contribution, therefore, is to show for various traffic mixes with given per-flow loss constraints that EDF offers consistently larger schedulable regions than GPS, both in the single-hop and multihop setting. As our final contribution, we argue that the use of GPS for statistical delay support is inherently problematic. We demonstrate that achieving the maximal schedulable regions under GPS could necessitate dynamic resynchronization of the GPS weights, an operation considered infeasible for practical implementation. I.

In this paper, we present a network service specifically designed for multimedia servers. It uses a histogram based traffic characterization and an overload control protocol to eliminate packet losses in the network while providing heterogeneous statistical QoS. The key contribution of our protocol lies in combining open-loop and feedback-based control to: (1) provide heterogeneous QoS to clients in networking environments consisting of switches that may not have any scheduling support; and (2) migrate the functionality of discarding packets, in the event of congestion, to the sources which understand the semantics of the data. The protocol is efficient, makes very few assumptions about the underlying network, is realizable on current switching hardware (supportingFCFS scheduling), and is completely integrated with the architecture of a multimedia server. 1 Introduction A common feature in a wide variety of multimedia applications is their requirement for storing, retrieving, and tran...