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

I.J.B.F. Adan (Corresponding author), B. Hathaway, V.G. Kulkarni

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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.

Originele taal-2Engels
Pagina's (van-tot)113-142
Aantal pagina's30
TijdschriftQueueing Systems: Theory and Applications
Volume91
Nummer van het tijdschrift1-2
Vroegere onlinedatum28 okt 2018
DOI's
StatusGepubliceerd - 15 feb 2019

Vingerafdruk

Queue
Numerical analysis
Customers
Performance Measures
Call Centres
Waiting Time
Class
M/G/1 Queue
Queue Length
Criticality
Percentage
Numerical Analysis
Approximation

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On first-come, first-served queues with two classes of impatient customers. / Adan, I.J.B.F. (Corresponding author); Hathaway, B. ; Kulkarni, V.G.

In: Queueing Systems: Theory and Applications, Vol. 91, Nr. 1-2, 15.02.2019, blz. 113-142.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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