Service Systems with Finite and Heterogeneous Customer Arrivals

Rowan Wang (), Oualid Jouini () and Saif Benjaafar ()
Additional contact information
Rowan Wang: Lee Kong Chian School of Business, Singapore Management University, Singapore 178899
Oualid Jouini: Laboratoire Génie Industriel, Ecole Centrale Paris, 92290 Châtenay-Malabry, France
Saif Benjaafar: Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455; and Engineering Systems and Design, Singapore University of Technology and Design, Singapore 138682

Manufacturing & Service Operations Management, 2014, vol. 16, issue 3, 365-380

Abstract: We consider service systems with a finite number of customer arrivals, where customer interarrival times and service times are both stochastic and heterogeneous. Applications of such systems are numerous and include systems where arrivals are driven by events or service completions in serial processes as well as systems where servers are subject to learning or fatigue. Using an embedded Markov chain approach, we characterize the waiting time distribution for each customer, from which we obtain various performance measures of interest, including the expected waiting time of a specific customer, the expected waiting time of an arbitrary customer, and the expected completion time of all customers. We carry out extensive numerical experiments to examine the effect of heterogeneity in interarrival and service times. In particular, we examine cases where interarrival and service times increase with each subsequent arrival or service completion, decrease, increase and then decrease, or decrease and then increase. We derive several managerial insights and discuss implications for settings where such features can be induced. We validate the numerical results using a fluid approximation that yields closed-form expressions.

Keywords: queueing systems; finite arrivals; heterogeneous interarrival and service times; transient analysis; fluid approximation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormsom:v:16:y:2014:i:3:p:365-380

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