The information-theoretic capacity of discrete-time queues

The information-theoretic capacity of continuous-time queues was analyzed recently by Anantharam and Verdu (see ibid. vol.42, p.4-18, 1996). Along similar lines, we analyze the information-theoretic capacity of two models of discrete-time queues. The first model has single packet arrivals and depart...

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Bibliographic Details
Published in:IEEE transactions on information theory 1998-03, Vol.44 (2), p.446-461
Main Authors: Bedekar, A.S., Azizoglu, M.
Format: Article
Language:English
Subjects:
Channel capacity
Exponential distribution
Information
Information analysis
Information rates
Information theory
Mathematical models
Queueing analysis
Random variables
Solid modeling
Theory
Time
Timing
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Summary:The information-theoretic capacity of continuous-time queues was analyzed recently by Anantharam and Verdu (see ibid. vol.42, p.4-18, 1996). Along similar lines, we analyze the information-theoretic capacity of two models of discrete-time queues. The first model has single packet arrivals and departures in a time slot and independent packet service times, and is the discrete-time analog of the continuous-time model analyzed by Anantharam and Verdu. We show that in this model, the geometric service time distribution plays a role analogous to that of the exponential distribution in continuous-time queues, in that, among all queues in this model with a given mean service time, the queue with geometric service time distribution has the least capacity. The second model allows multiple arrivals in each slot, and the queue is modeled as serving an independent random number of packets in each slot. We obtain upper and lower bounds on the capacity of queues with an arbitrary service distribution within this model, and show that the bounds coincide in the case of the queue that serves a geometrically distributed number of packets in each slot. We also discuss the extremal nature of the geometric service distribution within this model.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.661496