Performance analysis of a two-node computing cluster

• A performance model for a two-node computing cluster is studied.
• Customers’ impatience is considered for an M/M/2 queue with synchronous single working vacation.
• Explicit expressions are derived by using hypergeometric function and the generating function approach.
• The steady-state probabilities of the server, mean waiting time in the queue and queue length are obtained.
• Key performance measures such as sojourn time of a customer and the proportion of customers served are obtained.

This paper proposes a queueing model for the performance evaluation of a computing cluster. Requests arrive to the configurations according to a Poisson process at rate λ. There is a load balancing hardware in front of two servers to route requests to a free server if any. The service is commenced according to the first-come-first-served (FCFS) principle. The system can be either in the normal state or in the working vacation state. The service time of each customer during the normal state is exponentially distributed. We develop the balance equations for the steady-state probabilities and solve the equations by using the generating function and hypergeometric function. We obtain some performance measures for the system, such as the steady-state probabilities of the servers, the mean system sizes, the mean sojourn time of a customer served as well as the proportion of customers served and the rate of abandonment due to impatience. Finally, some numerical results are presented to demonstrate effects of some parameters on these performance measures of the system.