摘要
We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.
We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.
基金
Supported by the National Natural Science Foundation of China(No.11671404)
the Fundamental Research Funds for the Central Universities of Central South University 2016zzts014
