On value functions for FCFS queues with batch arrivals and general cost structures

Esa Hyytiä; Rhonda Righter; Jorma Virtamo; Lauri Viitasaari

doi:10.1016/j.peva.2020.102083

On value functions for FCFS queues with batch arrivals and general cost structures

Esa Hyytiä^*, Rhonda Righter, Jorma Virtamo, Lauri Viitasaari

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We develop a unified framework for analyzing and optimizing costs for systems of FCFS queues with batch arrivals, setup delays and a general nonlinear cost structure that includes costs associated with energy used, setup times and Quality of Service (QoS) measures. We focus on the M^X/G/1 and Geo^X/G/1 queues with i.i.d. service times, but our results hold also for arbitrary i.i.d. batch structures where service times within a batch may depend on the batch size and have different, possibly dependent, distributions. We use the notion of value functions from the theory of Markov decision processes (MDPs), along with exponential cost functions, to develop the notion of, and simple expressions for, value generating functions. These can be used to find efficient energy control and job dispatching policies.

Original language	English
Article number	102083
Journal	Performance Evaluation
DOIs	https://doi.org/10.1016/j.peva.2020.102083
Publication status	Accepted/In press - 1 Jan 2020
MoE publication type	A1 Journal article-refereed

Keywords

Batch arrivals
Generating function
Geo/G/1
M/G/1
Value function

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10.1016/j.peva.2020.102083

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Hyytiä, E., Righter, R., Virtamo, J., & Viitasaari, L. (Accepted/In press). On value functions for FCFS queues with batch arrivals and general cost structures. Performance Evaluation, [102083]. https://doi.org/10.1016/j.peva.2020.102083

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abstract = "We develop a unified framework for analyzing and optimizing costs for systems of FCFS queues with batch arrivals, setup delays and a general nonlinear cost structure that includes costs associated with energy used, setup times and Quality of Service (QoS) measures. We focus on the MX/G/1 and GeoX/G/1 queues with i.i.d. service times, but our results hold also for arbitrary i.i.d. batch structures where service times within a batch may depend on the batch size and have different, possibly dependent, distributions. We use the notion of value functions from the theory of Markov decision processes (MDPs), along with exponential cost functions, to develop the notion of, and simple expressions for, value generating functions. These can be used to find efficient energy control and job dispatching policies.",

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