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.
Highlights
In this paper, we analyze queueing systems with different classes of customers who may abandon the system if their waiting time exceeds their patience time, i.e., the maximum amount of time they are willing to wait before abandoning the system
We do this by characterizing the performance of FCFS systems with two customer classes that may differ from each other in both their distribution of service times and their distribution of patience times
Our analysis demonstrates that accounting for differences across classes in the distribution of customers’ service times and patience times is critical, as the performance of our system differs considerably from a system where only the service time distribution varies across classes
Summary
We analyze queueing systems with different classes of customers who may abandon (renege from) the system if their waiting time exceeds their patience time, i.e., the maximum amount of time they are willing to wait before abandoning the system. We do this by characterizing the performance of FCFS systems with two customer classes that may differ from each other in both their distribution of service times and their distribution of patience times. The second system is an M/M/c+M queue where customers across classes may differ in their exponentially distributed patience times, but all customers share the same exponentially distributed service times For both systems, the authors obtain the LT of the virtual waiting time for each of the k classes by exploiting the level-crossing technique in [8] and [9]. If service does not start before the patience time expires, the customer leaves without service
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