Appointment-driven queueing systems with non-punctual customers

Oualid Jouini (), Saif Benjaafar, Bingnan Lu, Siqiao Li and Benjamin Legros ()
Additional contact information
Oualid Jouini: Université Paris-Saclay
Saif Benjaafar: UMN - University of Minnesota System
Bingnan Lu: UMN - University of Minnesota System
Siqiao Li: Shangaï Jiao Tong University [Shangaï]
Benjamin Legros: Métis Lab EM Normandie - EM Normandie - École de Management de Normandie = EM Normandie Business School

Post-Print from HAL

Abstract: We consider a single-server queueing system where a finite number of customers arrive over time to receive service. Arrivals are driven by appointments, with a scheduled appointment time associated with each customer. However, customers are not necessarily punctual and may arrive either earlier or later than their scheduled appointment times or may not show up at all. Arrival times relative to scheduled appointments are random. Customers are not homogeneous in their punctuality and show-up behavior. The time between consecutive appointments is allowed to vary from customer to customer. Moreover, service times are assumed to be random with a γ -Cox distribution, a class of phase-type distributions known to be dense in the field of positive distributions. We develop both exact and approximate approaches for characterizing the distribution of the number of customers seen by each arrival. We show how this can be used to obtain the distribution of waiting time for each customer. We prove that the approximation provides an upper bound for the expected customer waiting time when non-punctuality is uniformly distributed. We also examine the impact of non-punctuality on system performance. In particular, we prove that non-punctuality deteriorates waiting time performance regardless of the distribution of non-punctuality. In addition, we illustrate how our approach can be used to support individualized appointment scheduling.

Date: 2022-01-09
References: Add references at CitEc
Citations:

Published in Queueing Systems, 2022, 101 (1), pp.1-56. ⟨10.1007/s11134-021-09724-9⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03605423

DOI: 10.1007/s11134-021-09724-9

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().