An Approximation to the Distribution and the Moments of the Number of Events in Markovian Arrival Processes

Abstract

In this paper, we propose to approximate the distribution and the moments of the number of events of a Markovian arrival process (MAP) in a time interval (0, t] by those of MAP events in an Erlang distributed random time interval. We present simple expressions for the later and show that when the order of Erlang distribution is high, the approximation is fairly accurate. The accuracy and computational efficiency of the proposed Erlangian approximation is compared with the uniformization method, and it is shown that the Erlangian method can be a useful tool in approximating the cumulative distribution function and moments of the number of MAP events.

Keywords:

• Erlangian approximation
• The distribution and moments of the number of events
• Transient Markovian arrival processes

Mathematics Subject Classification:

• Primary 60J22
• Secondary 60K15

ACKNOWLEDGMENT

Support for Jiandong Ren from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.