Renewal Approximations of the Switched Poisson Processes and Their Applications to Queueing Systems

The switched Poisson process (SPP), also known as the doubly stochastic Poisson process, has been widely used in the modelling of point processes whose rates vary subject to some random mechanism. The class of SPP includes a wide range of both renewal and non-renewal processes with squared coefficients of variation being larger than one. In this paper, we survey various approaches to approximate a non-renewal process by a renewal process. We derive the expressions for the first two moments of the inter-renewal time of a renewal process that approximates the SPP. We illustrate the quality of these approximations with numerical results in queueing applications. We believe that our approximations have potential applications in areas such as reliability, inventory control, telecommunications and maintenance.