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Service Systems with Finite and Heterogeneous Customer Arrivals

Author

Listed:
  • 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)

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.

Suggested Citation

  • Rowan Wang & Oualid Jouini & Saif Benjaafar, 2014. "Service Systems with Finite and Heterogeneous Customer Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 365-380, July.
  • Handle: RePEc:inm:ormsom:v:16:y:2014:i:3:p:365-380
    DOI: 10.1287/msom.2014.0481
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    References listed on IDEAS

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    Cited by:

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    2. Xu, Shuling & Hall, Nicholas G., 2021. "Fatigue, personnel scheduling and operations: Review and research opportunities," European Journal of Operational Research, Elsevier, vol. 295(3), pages 807-822.
    3. Song-Hee Kim & Ward Whitt & Won Chul Cha, 2018. "A Data-Driven Model of an Appointment-Generated Arrival Process at an Outpatient Clinic," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 181-199, February.
    4. Yun Fong Lim & Bingnan Lu & Rowan Wang & Wenjia Zhang, 2020. "Flexibly Serving A Finite Number of Heterogeneous Jobs in A Tandem System," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1431-1447, June.
    5. Setareh Boshrouei Shargh & Mostafa Zandieh & Ashkan Ayough & Farbod Farhadi, 2024. "Scheduling in services: a review and bibliometric analysis," Operations Management Research, Springer, vol. 17(2), pages 754-783, June.
    6. Oualid Jouini & Saif Benjaafar & Bingnan Lu & Siqiao Li & Benjamin Legros, 2022. "Appointment-driven queueing systems with non-punctual customers," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 1-56, June.

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