Equilibrium and Optimization in a Multi-server Queue with N-policy, Heterogeneous Information and Reneging

Considering two distinct streams of customers, we establish a multi-server queueing system with N-policy and reneging behavior in this paper. Specifically, the informed customers possess the knowledge of both the queue length and servers’ status, whereas the uninformed customers lack such information. The servers will go on vacation when the system becomes empty and resume working once N customers are accumulated. And all customers have the potential to renege if all servers are occupied. We thoroughly examine the two types of customers’ equilibrium and socially optimal joining strategies, along with an analysis of the customers’ total/effective joining rate and optimal social welfare. Our findings reveal that as the proportion of the informed customers increases, the total equilibrium joining rate first exceeds and then falls below the socially optimal joining rate. Additionally, revealing the information about the queue length and servers’ status, and setting a smaller N help improve the effective joining rate. Finally, there exists an appropriate level of information disclosure and a particular threshold N, each of which maximizes social welfare on its own. Such findings can offer valuable guidance for both the service provider and social planner in the relevant queueing systems.