On the optimal control of two queues with server setup times and its analysis
SIAM Journal on Computing
New Message Waiting Time in a Symmetric Polling System
Performance '84 Proceedings of the Tenth International Symposium on Computer Performance Modelling, Measurement and Evaluation
A Two-Queue Model with Semi-Exhaustive Alternating Service
Performance '87 Proceedings of the 12th IFIP WG 7.3 International Symposium on Computer Performance Modelling, Measurement and Evaluation
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A sojourn time analysis is provided for a cyclic-service tandem queue with general decrementing service which operates as follows: starting once a service of queue 1 in the first stage, a single server continues serving messages in queue 1 until either queue 1 becomes empty, or the number of messages decreases to k less than that found upon the server's last arrival at queue 1, whichever occurs first, where 1 @? k @? ~. After service completion in queue 1, the server switches over to queue 2 in the second stage and serves all messages in queue 2 until it becomes empty. It is assumed that an arrival stream is Poissonian, message service times at each stage are generally distributed and switch-over times are zero. This paper analyzes joint queue-length distributions and message sojourn time distributions.