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On the Value Function of the M/G/1 FCFS and LCFS Queues

Part of: Special processes

Published online by Cambridge University Press:  30 January 2018

Esa Hyytiä ,
Samuli Aalto ,
Aleksi Penttinen  and
Jorma Virtamo
Esa Hyytiä*
Affiliation:
Aalto University
Samuli Aalto*
Affiliation:
Aalto University
Aleksi Penttinen*
Affiliation:
Aalto University
Jorma Virtamo*
Affiliation:
Aalto University
*
∗ Postal address: Department of Communications and Networking, Aalto University, School of Electrical Engineering, PO Box 13000, 00076 Aalto, Finland.
∗ Postal address: Department of Communications and Networking, Aalto University, School of Electrical Engineering, PO Box 13000, 00076 Aalto, Finland.
∗ Postal address: Department of Communications and Networking, Aalto University, School of Electrical Engineering, PO Box 13000, 00076 Aalto, Finland.
∗ Postal address: Department of Communications and Networking, Aalto University, School of Electrical Engineering, PO Box 13000, 00076 Aalto, Finland.
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Abstract

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We consider a single-server queue with Poisson input operating under first-come–first-served (FCFS) or last-come–first-served (LCFS) disciplines. The service times of the customers are independent and obey a general distribution. The system is subject to costs for holding a customer per unit of time, which can be customer specific or customer class specific. We give general expressions for the corresponding value functions, which have elementary compact forms, similar to the Pollaczek–Khinchine mean value formulae. The results generalize earlier work where similar expressions have been obtained for specific service time distributions. The obtained value functions can be readily applied to develop nearly optimal dispatching policies for a broad range of systems with parallel queues, including multiclass scenarios and the cases where service time estimates are available.

Keywords

M/G/1FCFSLCFSvalue functionsojourn timemean delay

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90C40: Markov and semi-Markov decision processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1052 - 1071
Copyright
© Applied Probability Trust 

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