Multiclass state‐dependent service systems with returns. (11th June 2020)

• Record Type: Journal Article
• Authors: Barjesteh, Nasser; Abouee‐Mehrizi, Hossein
• Other Names: Baron Opher guestEditor.
• Is Part Of: Naval research logistics. Volume 68:Number 5(2021)
• Page Start: 631
• Page End: 662
• Publication Date: 2020-06-11
• Subjects: equilibrium analysis -- fluid approximation -- Markov chain -- state‐dependent queueing network; Logistics, Naval -- Periodicals; Supplies and stores -- Periodicals; 359.07
• DOI: 10.1002/nav.21908
• Languages: English
• ISSNs: 0894-069X

Abstract

Abstract: 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.