Analysis of a fork-join system with strategic customers

In real life, fork-join queuing systems can be employed to model a variety of systems including service systems, healthcare, project management, data processing, and manufacturing systems. In this thesis, we investigate the effect of the various information levels on the performance measures of a two-server fork-join queuing system with strategic customers. Strategic customers receive the information provided to them and make joining/balking decisions using this information upon their arrival. Customers arrive at the system as a pair of two, each of which is directed to one of the parallel servers if they decide to join the system. After the completion of the service, customers wait for each other and depart from the system together. %Therefore, the total time spent in the system by a pair is determined by the maximum of the two service durations. In this study, we examine three types of information structures: fully observable, partially observable, and unobservable. The level of the information provided to customers plays a significant role in their joining decision and therefore it impacts the performance of the entire system. In order to understand this impact, a set of performance measures are considered which are average utility, effective arrival (joining) rate, and expected waiting time of the customers. We derive the necessary mathematical expressions to calculate the performance measures of a two-server fork-join system for all three information structures. Moreover, a set of numerical experiments are performed with different values of the system parameters. The results show that additional information always increases the average utility of the customers. In most of the cases, the joining rate of the customers decreases as more information is provided to them. We identify the cases in which more information generates a higher effective arrival rate. Additionally, we provide a comprehensive analysis on the results of the experiments.