Title: Improving service system performance using estimates of waiting time probabilities

Authors: Akash Gupta; Debjit Roy; Jennifer A. Pazour

Addresses: Production and Quantitative Methods Area, Indian Institute of Management Ahmedabad, Gujarat 380015, India ' Production and Quantitative Methods Area, Indian Institute of Management Ahmedabad, Gujarat 380015, India ' Department of Industrial Engineering and Management Systems, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32816-2993, USA

Abstract: Queue length distributions provide insight into the impact of service system design changes that go beyond simple performance measure averages; however, such distributions are difficult to estimate when service times are not exponential. In this research, we model service systems using queuing networks and develop a continuous time Markov chain (CTMC) to compute the steady state probability distribution function for the number of customers and the waiting time probabilities in a network of GI/G/c queues. Using a generalised generator matrix, we evaluate the steady state probability of any number of customers in the queue. For a network of general queues, we link the queues using a parametric decomposition approach. Through two service sector examples, we illustrate that explicitly modelling the arrival and service rates as general distributions (rather than approximating them using Markovian distributions) can lead to significantly better resource allocations.

Keywords: logistics; healthcare services; GI/G/c queues; queuing networks; waiting time probability; service systems; Markov chains; system performance; system design; service rates; arrival rates.

DOI: 10.1504/IJAL.2015.068896

International Journal of Automation and Logistics, 2015 Vol.1 No.2, pp.150 - 175

Received: 31 Aug 2013
Accepted: 22 Feb 2014
Published online: 25 Apr 2015 *

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