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Multiclass state‐dependent service systems with returns
Author(s) -
Barjesteh Nasser,
AboueeMehrizi Hossein
Publication year - 2021
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21908
Subject(s) - workload , computer science , service system , service (business) , rework , queueing theory , markov chain , markov process , stability (learning theory) , operations research , system dynamics , mathematical optimization , computer network , mathematics , economics , statistics , economy , machine learning , artificial intelligence , embedded system , operating system
In this paper, we consider a service system facing several classes of customers in which the arrival rate and service time depend on the workload in the system, while the chance of return is a function of the service time. We first model the problem as a multiclass multiserver queueing network and investigate its stability by examining the conditions under which the Markov chain representing the network is positive recurrent. We then examine the impact of the relationship among the workload, service time, arrival rate, and the chance of return on the dynamics of the system using a fluid approach. We first characterize all equilibria of the system and show that the system may shift between several equilibrium states. We establish that all equilibria can be easily determined and demonstrate conditions under which an equilibrium is stable. We then prove that, surprisingly, the stability of an equilibrium and the congestion in the system may depend on the amount of time a customer spends outside of the system before returning for rework. However, we show that if the relationship between the workload and service time in a system facing a single class of customers is nondecreasing, the long‐run behavior of the system is not affected by how long it takes until a customer returns.