Queue Length Analysis of MAP/G/1 Queue UnderD-Policy

Ho Woo Lee · Kyoung Seok Song

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

We study the queue length distribution of a queueing system with MAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths will be derived from these transform results. A numerical example is provided.

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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.1987Stochastic Modelling and Analysis: A Computational Approach.1990A single-server queue with server vacations and a class of non-renewal arrival processes 1980The N/G/1 queue and its detailed analysis 1987Stochastic modelling and analysis: A computational approach,2005The BMAP/G/1 queue: A tutorial 1973Control Policies for a Single Server System

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2008The performance of the M/G/1 queue under the dyadic -policy and its cost optimization 2021The continuous (S,s,Se) inventory model with dual sourcing and emergency orders 2018A threshold policy in a Markov-modulated production system with server vacation: the case of continuous and batch supplies 2005BMAP/G/1 Queue UnderD-Policy: Queue Length Analysis

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