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On first-come, first-served queues with two classes of impatient customers

Author

Listed:
  • Ivo Adan

    (Eindhoven University of Technology)

  • Brett Hathaway

    (University of North Carolina at Chapel Hill)

  • Vidyadhar G. Kulkarni

    (University of North Carolina at Chapel Hill)

Abstract

We study systems with two classes of impatient customers who differ across the classes in their distribution of service times and patience times. The customers are served on a first-come, first-served basis (FCFS) regardless of their class. Such systems are common in customer call centers, which often segment their arrivals into classes of callers whose requests differ in their complexity and criticality. We first consider an M/G/1 + M queue and then analyze the M/M/k + M case. Analyzing these systems using a queue length process proves intractable as it would require us to keep track of the class of each customer at each position in the queue. Consequently, we introduce a virtual waiting time process where the service times of customers who will eventually abandon the system are not considered. We analyze this process to obtain performance measures such as the percentage of customers receiving service in each class, the expected waiting times of customers in each class, and the average number of customers waiting in queue. We use our characterization to perform a numerical analysis of the M/M/k + M system and find several managerial implications of administering a FCFS system with multiple classes of impatient customers. Finally, we compare the performance a system based on data from a call center with the steady-state performance measures of a comparable M/M/k + M system. We find that the performance measures of the M/M/k + M system serve as good approximations of the system based on real data.

Suggested Citation

  • Ivo Adan & Brett Hathaway & Vidyadhar G. Kulkarni, 2019. "On first-come, first-served queues with two classes of impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 113-142, February.
    • Handle: RePEc:spr:queues:v:91:y:2019:i:1:d:10.1007_s11134-018-9592-z
    DOI: 10.1007/s11134-018-9592-z
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    References listed on IDEAS

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    Cited by:

    1. Onno Boxma & Michel Mandjes, 2021. "Shot-noise queueing models," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 121-159, October.
    2. Onno Boxma & David Perry & Wolfgang Stadje, 2022. "Peer-to-Peer Lending: a Growth-Collapse Model and its Steady-State Analysis," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 233-258, October.
    3. D’Auria, Bernardo & Adan, Ivo J.B.F. & Bekker, René & Kulkarni, Vidyadhar, 2022. "An M/M/c queue with queueing-time dependent service rates," European Journal of Operational Research, Elsevier, vol. 299(2), pages 566-579.
    4. Ivo Adan & Onno Boxma & Jacques Resing, 2022. "Functional equations with multiple recursive terms," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 7-23, October.

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