Worst-case bounds on delay and backlog are derived for leaky bucket constrained sessions in arbitrary topology networks of generalized processor sharing (GPS) servers. The inherent flexibility of the service discipline is exploited to analyze broad classes of networks. When only a subset of the sessions are leaky bucket constrained, we give succinct per-session bounds that are independent of the behavior of the other sessions and also of the network topology. However, these bounds are only shown to hold for each session that is guaranteed a backlog clearing rate that exceeds the token arrival rate of its leaky bucket. A much broader class of networks, called consistent relative session treatment (CRST) networks is analyzed for the case in which all of the sessions are leaky bucket constrained. First, an algorithm is presented that characterizes the internal traffic in terms of average rate and burstiness, and it is shown that all CRST networks are stable. Next, a method is presented that yields bounds on session delay and backlog given this internal traffic characterization. The links of a route are treated collectively, yielding tighter bounds than those that result from adding the worst-case delays (backlogs) at each of the links in the route. The bounds on delay and backlog for each session are efficiently computed from a universal service curve, and it is shown that these bounds are achieved by "staggered" greedy regimes when an independent sessions relaxation holds. Propagation delay is also incorporated into the model. Finally, the analysis of arbitrary topology GPS networks is related to Packet GPS networks (PGPS). The PGPS scheme was first proposed by Demers, Shenker and Keshav (1991) under the name of weighted fair queueing. For small packet sizes, the behavior of the two schemes is seen to be virtually identical, and the effectiveness of PGPS in guaranteeing worst-case session delay is demonstrated under certain assignments. >

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A generalized processor sharing approach to flow control in integrated services networks: the multiple node case

Fair queuing is a technique that allows each flow passing through a network device to have a fair share of network resources. Previous schemes for fair queuing that achieved nearly perfect fairness were expensive to implement; specifically, the work required to process a packet in these schemes was O(log(n)), where n is the number of active flows. This is expensive at high speeds. On the other hand, cheaper approximations of fair queuing reported in the literature exhibit unfair behavior. In this paper, we describe a new approximation of fair queuing, that we call deficit round-robin. Our scheme achieves nearly perfect fairness in terms of throughput, requires only O(1) work to process a packet, and is simple enough to implement in hardware. Deficit round-robin is also applicable to other scheduling problems where servicing cannot be broken up into smaller units (such as load balancing) and to distributed queues.

Efficient fair queueing using deficit round-robin

Worst-case bounds on delay and backlog are derived for leaky bucket constrained sessions in arbitrary topology networks of generalized processor sharing servers. When only a subset of the sessions are leaky bucket constrained succinct per-session bounds that are independent of the behavior of the other sessions and also of the network topology are given. However, these bounds are only shown to hold for each session that is guaranteed a backlog clearing rate that exceeds the token arrival rate of its leaky bucket. When all of the sessions are leaky bucket constrained, a much larger class of networks called consistent relative session treatment networks is analyzed. The session i route is treated as a whole, yielding tighter bounds than those that result from adding the worst-case delays (backlogs) at each of the servers in the route. The bounds on delay and backlog for each session are computed and shown to be achieved by staggered regimes when an independent sessions relaxation holds. Propagation delay is also incorporated into the model. >

/pdf/a-generalized-processor-sharing-approach-to-flow-control-in-1g5a436ph7.pdf

A generalized processor sharing approach to flow control in integrated services networks-the multiple node case

Originating from basic research conducted in the 1970's and 1980's, the parallel and distributed simulation field has matured over the last few decades. Today, operational systems have been fielded for applications such as military training, analysis of communication networks, and air traffic control systems, to mention a few. The article gives an overview of technologies to distribute the execution of simulation programs over multiple computer systems. Particular emphasis is placed on synchronization (also called time management) algorithms as well as data distribution techniques.

/pdf/parallel-and-distributed-simulation-systems-2ovm9qn1cd.pdf

Parallel and Distributed Simulation Systems

コンピュータ・サイエンス : ACM computing surveys

Binary exponential backoff is a randomized protocol for regulating transmissions on a multiple-access broadcast channel. Ethernet, a local-area network, is built upon this protocol. The fundamental theoretical issue is stability: Does the backlog of packets awaiting transmission remain bounded in time, provided the rates of new packet arrivals are small enough? It is assumed n ≥ 2 stations share the channel, each having an infinite buffer where packets accumulate while the station attempts to transmit the first from the buffer. Here, it is established that binary exponential backoff is stable if the sum of the arrival rates is sufficiently small. Detailed results are obtained on which rates lead to stability when n = 2 stations share the channel. In passing, several other results are derived bearing on the efficiency of the conflict resolution process. Simulation results are reported that, in particular, indicate alternative retransmission protocols can significantly improve performance.

Stability of binary exponential backoff

Fair Queuing is a novel queuing discipline with important applications to data networks that support variable-size packets and to systems where the cost of preempting jobs from service is high. The disciphne controls a single server shared by N job arrival streams with each stream allotted a separate queue. After every job completion, the server is assigned to serve, without possibihty of interruption, the job at the head of one of the queues (as soon as at least one job appears in the system). Fair Queuing is designed to handle arbitrary job arrival sequences with essentially no a priori knowledge of their attributes. such that each stream receives its 'Lfam share" of serwce. In this paper, we consider two variants of the fair queuing discipline, and rigorously establish their fairness wa sample path comparisons with the head-of-line processor sharing disclphne, a mathematical idealization that prowdes a fairness paradigm. An efficient Implementation of one of the fair queuing disciplines is presented, In passing, a new, fast method for simulating processor sharing is derived. Simulation results are presented to further explore the comparison between fair queuing and processor sharing.

How fair is fair queuing

A communications system and method of ordered borrowing which facilitates dynamic access to a global channel set that has been partitioned into subsets, with each cell of the system being assigned a particular subset of the channel set. The assignment of channel subsets is performed in such a way as to respect various constraints imposed by the physical layout. Calls originating in a cell are first assigned to the channels allocated to the base station of that cell, in an order determined by the cell. Once the allotted channels are exhausted, i.e. in the busy state, the cell attempts to borrow channels from those allotted to the base stations of neighboring cells in a specified order. The borrowing cell borrows a specified number of channels from each neighbor before returning to a particular cell to borrow additional channels. The channels borrowed from a neighbor are accessed in an order which is substantially the reverse of the order in which they are accessed by the owner cell. This prescribes, for each cell, a prespecified order in which the entire set of channels may be accessed by calls originating in that cell.

Apparatus and method for dynamic resource allocation in wireless communication networks utilizing ordered borrowing

A problem related to the decentralized control of a multiple access channel is considered: Suppose k stations from an ensemble of n simultaneously transmit to a multiple access channel that provides the feedback 0, 1, or 2+, denoting k = 0, k = 1, or k ≥ 2, respectively. If k = 1, then the transmission succeeds. But if k ≥ 2, as a result of the conflict, none of the transmissions succeed. An algorithm to resolve a conflict determines how to schedule retransmissions so that each of the conflicting stations eventually transmits singly to the channel. In this paper, a general model of deterministic algorithms to resolve conflicts is introduced, and it is established that, for all k and n (2 ≤ k ≤ n), O(k(log n)/(log k)) time must elapse in the worst case before all k transmissions succeed.

A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels

In emerging communication networks (B-ISDN based on asynchronous transfer mode (ATM) technology), a single link may carry traffic for thousands of connections with different traffic parameters and quality-of-service requirements. High-speed links, coupled with small packet/cell sizes, require efficient switch architectures that can handle cell arrivals and departures every few microseconds, or faster. This paper presents a collection of self-clocked fair queueing (SCFQ) architectures amenable to efficient hardware implementation in network switches. Exact and approximate implementations of SCFQ efficiently handle a moderate range of connection bandwidth parameters, while hierarchical arbitration schemes scale to a large range of throughput requirements. Simulation experiments demonstrate that these architectures divide link bandwidth fairly on a small time scale, preserving connection bandwidth and burstiness properties.

Albert G. Greenberg

Papers

Stability of binary exponential backoff

How fair is fair queuing

Apparatus and method for dynamic resource allocation in wireless communication networks utilizing ordered borrowing

A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels

Hardware-efficient fair queueing architectures for high-speed networks