Approximate Analysis of the Queuing System with Heterogeneous Servers and N-Policy

In this paper, we propose an approximate method to investigate the Markovian queuing system with two separate pools of heterogeneous servers (HS) under N-policy. It is assumed that fast servers (F-servers) remain awake all the time while slow servers (S-servers) will go to sleep independently when number of calls in the buffer less than some threshold. At the end epoch of a sleep period, if the number of the calls gathered in the system buffer reaches or exceeds a given threshold, the corresponding S-server will wake up independently; otherwise, the S-server will begin another sleep period. An approximate method is applied under the condition that the sleep rates is essentially less than both arrival intensity of calls and their service intensity. The joint probability distribution of the number of calls in system and number of busy S-servers is determined by simple computational procedures. Illustrative numerical examples show the high accuracy of the proposed approximate method.