PRIMARY CATEGORY: D.4.8 Performance (Queueing Theory) C R O S S R E F E R E N C E S : G.m Miscellaneous (Queueing Theory), D.4.8 Performance (Stochastic Analysis), F.2.2 Nonnumerical Algorithms and Problems (Sequencing and Scheduling), C.2.1 Network Architecture and Design G E N E R A L T E R M S : DESIGN, PERFORMANCE, THEORY, VERIFICATION Author(s): Shivendra S. Panwar (Polytechnic Univ., Brooklyn, NY); Don Towsley (Univ. of Massachutsetts, Amherst); Jack K. Wolf (Univ. of California at San Diego, La Jolla). Optimal scheduling policies for a class of Queues with customer deadlines to the beginning of service Title Journal : J. ACM, Vol. 35, No. 4 (Oct. 1988), 832-844. This paper treats the problem of queueing packets which have an assigned expiration date. If a packet does not begin processing within the specified time limit, it is discarded as useless. The primary example is transmission of voice or video frames over a packet-switched network, where the illusion of realtime transmission is to be maintained. The occasional loss of a packet will reduce transmission quality, but the voice or video reception should remain intelligible. The formal results are as follows: A shortest time to extinction (STE) policy services the customer nearest its completion deadline, if no customer is already being serviced. A shortest time to ezlinction with inserted idle time (STEI) policy also services the customer nearest its completion deadline, though it may choose to sit idle before servicing the next customer. A scheduling policy is optimal within its class if it is minimal w.r.t, the expected number of discarded packets. 1. For a continuous-time nonpreemptive queue with an exponential distribution of arrivals, a general distribution of service times, and a general distribution of deadlines (M/G/1 + G queue), the STE policy is optimal among policies not inserting idle-times. 2. As above, except inserted idle-times are permitted, STEI policies will approach optimality. 3. For a discrete-time nonpreemptive queue with a general distribution of arrivals, unit service time, and a general distribution of deadlines (G/D/1 + G queue), the STE policy is optimal even with inserted idle-times permitted. The proven results are supplemented by some approximations of the expected losses incurred by STE vs. FCFS and STEI under various parameters. The authors were unable to construct an STEI policy superior to STE. These results are of fundamental importance in queueing theory. The classes of queues and policies under consideration are quite basic, yet results in this field are scarce even under simple conditions. The fact that STE and STEI policies are optimal seems to be the "intuitively most plausible" result. Unfortunately the proofs required a significant amount of notation, even though the proof ideas were straightforward. The level of (un)readability is typical of the Journal of the ACM, though a better presentation would be difficult. A less frivolous complaint is that the results do not extend further: can one construct an STEI policy that is optimal for the M/G/1 + G queue? Result ~2 uses an existence proof which can construct an STEI policy to match the performance of any other policy. No optimal policy is presented. Alternatively one might show that some intuitively simple STEI policies are suboptimal. Regarding the original intent of the paper, the distribution of discarded packets is worth considering. The transmission will not be intelligible if the losses are clumped together. -- Carl G. Ponder, Livermore, CA. Performance Evaluation Review Vol. 18 #3, November 1990

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