|M.Sc Student||Nakibly Guy|
|Subject||On the Reliability Exponents of Two Discrete-Time Timing|
|Department||Department of Electrical Engineering||Supervisor||Dr. Shraga Bross|
The information-theoretic capacity of continuous-time queues was first analyzed by Anantharam and Verdu. Arikan proves in the random-coding and sphere-packing bounds on the reliability exponent of the Exponential-Server Timing Channel (ESTC) which is the queue having the lowest capacity among all /G/1 queues with fixed mean service time. Thus, Arikan's result determines the reliability exponent of the /M/1 queue for all rates above the critical rate. Recently, Wagner and Anantharam determined the zero-rate exponent of the ESTC and obtained the straight-line bound for this channel.
Bedekar and Azizoglu analyze the information-theoretic capacity of two discrete-time queuing models. The first model allows single packet arrival and single packet departure in a slot unit, while the service times are independent identically distributed with fixed mean. The second model allows multiple arrivals as well as multiple departures in each slot, and the queue is modeled as serving an independent random number of packets in each slot. In this context Bedekar and Azizoglu consider the geometric server queue and its corresponding timing capacity is determined for both models.
This work considers the reliability exponents of the two discrete-time single-server timing channel models studied by Bedekar and Azizoglu. Specifically, the reliability exponents are determined for rate zero as well as for all rates between the corresponding critical rate and channel capacity. In both models, for rates between zero and the critical rate, we provide random-coding lower bound and straight-line combined with sphere-packing upper bound on the reliability exponent.