On the advantage of being the first server
Management Science
A resource allocation queueing fairness measure: properties and bounds
Queueing Systems: Theory and Applications
Quantifying fairness in queuing systems: Principles, approaches, and applicability
Probability in the Engineering and Informational Sciences
Analysis and Comparison of Queues with Different Levels of Delay Information
Management Science
User equilibria for a parallel queueing system with state dependent routing
Queueing Systems: Theory and Applications
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Consider two servers of equal service capacity, one serving in a first-come first-served order (FCFS), and the other serving its queue in random order. Customers arrive as a Poisson process and each arriving customer observes the length of the two queues and then chooses to join the queue that minimizes its expected queueing time. Assuming exponentially distributed service times, we numerically compute a Nash equilibrium in this system, and investigate the question of which server attracts the greater share of customers. If customers who arrive to find both queues empty independently choose to join each queue with probability 0.5, then we show that the server with FCFS discipline obtains a slightly greater share of the market. However, if such customers always join the same queue (say of the server with FCFS discipline) then that server attracts the greater share of customers.