A MULTI-SERVER QUEUEING MODEL WITH MARKOVIAN ARRIVALS AND MULTIPLE THRESHOLDS

Srinivas Chakravarthy

11 citations0/0 files storedAsia Pacific Journal of Operational Research

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

We consider a multi-server queueing model in which arrivals occur according to a Markovian arrival process (MAP). There is a single-server and additional (backup) servers are added or removed depending on sets of thresholds. The service times are assumed to be exponential and the servers are assumed to be homogeneous. A comparison of this model to the classical MAP/M/c queueing model through an optimization problem yields some interesting results that are useful in practical applications. For example, we notice that positively correlated arrival process appears to benefit with the threshold type queueing model. We also give the minimum delay costs and the associated maximum setup costs so that the threshold type queueing model is to be preferred over the classical MAP/M/c model.

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References

1991New results on the single server queue with a batch markovian arrival process 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1999Fundamentals of Queueing Theory 1963Queueing Systems with a Removable Service Station 1968Optimal Operating Policies for M / G /1 Queuing Systems 1984Optimal control of a queueing system with two heterogeneous servers 1969Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs 2000A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity

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2006Computational analysis of the maximal queue length in the MAP/M/c retrial queue

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