An Analysis of the Join the

This paper presents an accurate analytical model for evaluating the performance of the Join the Shortest Queue (JSQ) policy. The system considered consists of N identical queues with infinite buffers, and each of the queues has one server. Job arrival process is assumed to be Poisson. Service times are assumed to be exponentially distributed. When a job arrives at the system, it is sent to the queue with the smallest number of jobs. Ties are broken by selecting randomly one of the queues with minimal number of jobs. Exact analysis of the JSQ policy is known to be very difficult, and our analytical model for JSQ policy gives very close approximations. A birth-death Markov process is used to model the evolution of the number of jobs in the system. An iterative procedure is devised to estimate the state transition rates. Average job response time is used as the performance measure. Extensive simulations are performed and compared with the analytical results. Our results show that this method provides very accurate estimates (within 3.5%) of the average job response times for N up to 64.