Tandem Queues with Impatient Customers

30 Pages Posted: 15 Feb 2018 Last revised: 20 Jun 2019

See all articles by Jianfu Wang

Jianfu Wang

Nanyang Technological University (NTU) - Nanyang Business School

Hossein Abouee Mehrizi

University of Waterloo

Opher Baron

University of Toronto - Operations Management

Oded Berman

University of Toronto - Operations Management

Date Written: February 2, 2018

Abstract

This paper studies a Markovian two-station tandem queueing network with impatient customers. Queueing networks with abandonment are common in many industries, e.g., call centers and healthcare. Therefore, their management has received much attention. The resulting model is a level-dependent quasi-birth-and-death (LDQBD) process. Such models are considered analytically intractable and require numerical methods for their solution. We study a specific type of LDQBD process, where the total abandonment rate increases with the number of waiting customers leading to the level-dependent feature. We analyze an equivalent last-come-first-serve system to develop a recursive relation in our LDQBD process, reducing the problem to solving quadratic matrix equations, for which efficient and exact numerical methods exist. We further simplify the analysis by combining the recursive renewal reward theorem with Queueing and Markov chain decomposition (QMCD), so that we only need to solve one quadratic matrix equation instead of infinite ones caused by the system's level-dependent feature. We develop an exact numerical method to evaluate various performance measures of a tandem queueing network with abandonment. Our method is applicable to the analysis of queueing networks with abandonment under settings with diverse features and in various service disciplines.

Keywords: tandem queue, impatient customers, abandonment, flexible servers

Suggested Citation

Wang, Jianfu and Abouee Mehrizi, Hossein and Baron, Opher and Berman, Oded, Tandem Queues with Impatient Customers (February 2, 2018). Rotman School of Management Working Paper No. 3116815. Available at SSRN: https://ssrn.com/abstract=3116815 or http://dx.doi.org/10.2139/ssrn.3116815

Jianfu Wang (Contact Author)

Nanyang Technological University (NTU) - Nanyang Business School ( email )

Singapore, 639798
Singapore

Hossein Abouee Mehrizi

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Opher Baron

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Oded Berman

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

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