A simple approach to the map/d/s queue

Tetsuya Takine

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

We provide a simple approach to analyze the stationary MAP/D/s queue, where customers are served under the FCFS discipline. Assuming a cyclic assignment of customers to servers, we first characterize the sojourn time distribution, and with this, the queue length distribution immediately after departures is obtained. Further, utilizing the relationship between the time-average queue length distribution and the customer-average queue length distribution at departures, we obtain a numerically feasible formula for the stationary queue length mass function

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1990A single-server queue with server vacations and a class of non-renewal arrival processes 1988A stable recursion for the steady state vector in markov chains of m/g/1 type 1985Opsearch 1994The workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority 2001Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions 1994Mean waiting times in nonpreemptive priority queues with Markovian Arrival and i.i.d. service Processes 1998On the relationship between queue lengths at a random instant and at a departure in the stationary queue with bmap arrivals 1982The c — Server Queue with Constant Service Times and a Versatile Markovian Arrival Process

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