Optimal staffing for ticket queues

Li Xiao (), Susan H. Xu, David D. Yao () and Hanqin Zhang ()
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Li Xiao: Tsinghua University
Susan H. Xu: The Pennsylvania State University
David D. Yao: Columbia University
Hanqin Zhang: National University of Singapore

Queueing Systems: Theory and Applications, 2022, vol. 102, issue 1, No 13, 309-351

Abstract: Abstract Ticket queues are popular in many service systems. Upon arrival, each customer is issued a numbered ticket and receives service on a first-come-first-served basis according to the ticket number. There is no physical queue; customers may choose to walk away and return later (before their numbers are called) to receive service. We study the problem of optimal staffing in such a system with two capacity levels, where the staffing decision can only be based on ticket numbers, as opposed to the physical queue length in a traditional system. Using renewal reward theorem, we first derive the long-run average total cost (including customer delay and abandonment costs, operating cost and cost for changing staffing levels) and then obtain the optimal solution using fractional programming. In addition, we pursue a random-walk analysis, which leads to some highly accurate approximations.

Keywords: Ticket queue; Customer abandonment; Markov chain; Optimal staffing; Fractional programming; Random walk; 60K20; 60K25; 60K30; 90B22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11134-022-09854-8

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