Thanks to technology, the queue has almost become a thing of the past. With the internet, booking train tickets, bus tickets, and also for leisure activities, such as booking tickets for movies, the hassle of waiting in a queue has almost disappeared.
However, there are still certain services that make you to wait, either physically or online, for a long period of time. These include sectors such as healthcare, telecommunications, call centers, etc.
One of the main issues in handling queued customers, is the impatience of the customers. Many customers, because of their impatience, tend to leave the queue before receiving service. Customers may abandon the queue if their waiting time exceeds a threshold. This behaviour is known as impatience or reneging. Efficient management of these queues is particularly challenging when customers are served on what is known as a first-come, first-served (FCFS) basis, regardless of their class. In this paper, the performance of FCFS queuing systems with multiclass impatient customers is characterised.
The study of queuing systems is a branch in mathematics that deals with the behaviour of queues, and includes the customer arrival, time for waiting, receiving service, and departure.
Previous studies on effective queuing systems have focused on only a single-class, or two classes of queuing systems. This is not practical, as in reality there are multiple classes of customers with multiple servers.
In this study, the authors Mr. Vinay Kumar and Prof. Neelesh Shankar Upadhye from the Department of Mathematics, Indian Institute of Technology (IIT) Madras, Chennai, India, have considered a first-come, first-served (FCFS) queuing system, with multiple classes of customers, with multiple servers. To the best of the authors’ knowledge, this is the first time multiple classes of customers with multiple servers has been analysed.
The authors have analysed two queuing models, with customer abandonment, namely – M/G/1 + M, and M/M/m + M. These are Markovian/Poisson distribution queuing models.
M/G/1 + M represents a single-server queue, and M/M/m + M represents a multi-server queuing system.
Steady-state analyses were derived for the two systems, and a case where all customer classes shared the same mean service time was explored. Performance measures in the steady state are derived for both systems.
Numerical analysis was done for the multi-server queuing system using the proposed characterisations. The actual and simulated multi-server systems were then compared using steady-state metrics, including the proportion of served customers in each class, the mean waiting times for customers in each class, and the system throughput derived analytically.
To illustrate the practical relevance of the results derived in this study, the authors considered an online market place call center that handles service requests for general inquiries, technical support, billing and payments, product returns and exchanges, complaints, and escalations.
The numerical results of this study, and the case study for a call center, show that this multi-class queuing system with impatient customers can be applied to various real-world scenarios, such as, call centers and airport queue management systems, where different types of service requests are made. This is especially relevant when customers have different patience time distributions. The system allows for a subset of service agents to be specifically trained to handle certain types of customers, leading to improved efficiency and customer satisfaction.
By understanding the behaviour of queuing systems, managers can make informed decisions about resource allocation, staffing, and customer service strategies. This can result in better customer experiences, reduced waiting times, and improved system performance.
One of the important findings of this study was that if the number of servers was kept constant, the system’s performance reached optimal levels with a specific number of customer classes. Future studies could be done to determine the ideal number of classes that can maximise performance within the constraints of a given server configuration.
Prof. G. Ravindran from the Indian Statistical Institute (ISI) Chennai, India, acknowledged the importance of this work with the following comments: “Prof. Upadhye’s research tackles a highly relevant and complex problem in queueing theory: modeling service systems where customers—classified into multiple types—may lose patience and leave the queue. By effectively integrating the concepts of customer heterogeneity and impatience within a first-come, first-served framework, the paper offers valuable insights. The use of simulation to study such systems—where analytical solutions are often intractable—is both methodologically sound and practically meaningful. The findings are academically rigorous and hold significant relevance for optimizing real-world operations in domains such as telecommunications, healthcare, and customer service centres.”
Article by Akshay Anantharaman
Click here for the original link to the paper
