On a Single-Server Finite Queuing Model with State-Dependent Arrival and Service Processes

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

Abstract

This paper generalizes the M/G/1 queuing process by considering both the arrival and the service rates as being essentially arbitrary functions of the current number of customers in the system, and by assuming, moreover, that the amount of service demanded by a customer is conditioned by the queue length at the moment service is begun for that customer. Taking the imbedded Markov chain approach, the paper proposes a method for calculating (1) the limiting probability distribution of the congestion and (2) the expected value of the time needed to complete a service. An expression for the distribution of the waiting time is then given and its first moment deduced.

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References

1963Introduction to the Theory of Queues.1967Queues with State-Dependent Stochastic Service Rates 1967A Simple Proof of: L = λW

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2014A single-server Markovian queuing system with discouraged arrivals and retention of reneged customers 2012Analysis of finite-buffer state-dependent bulk queues 1982Application of level crossing analysis to discrete state processes in queueing systems 1994A unified algorithm for computing the stationary queue length distributions inM(k)/G/1/N and GI/M(k)/1/N queues 2014Service Systems with Finite and Heterogeneous Customer Arrivals 2001Analysis of an inventory system under backorder correlated deterministic demand and geometric supply process 2006Analysis and Computational Algorithm for Queues with State-Dependent Vacations I: G/M(n)/1/K 1998On the analysis of single server finite queue with state dependent arrival and service processes: $M(n)/G(n)/1/K$

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