A generalized M/G/1 queuing system is considered where the efficiency of the server varies as the number of customers served in a busy period increases due to server fatigue or service enforcement. More specifically, the k-th arriving customer within a busy period has the random service requirement Vk where the 0-th customer initiates the busy period and Vk (k=0,1,2,...) are mutually independent but may have different distributions. This model includes an M/G/1 queuing model with delayed busy period as a special case where Vk (k ≧ 1) are independent, identically distributed (i.i.d.) Transform results are obtained for the system idle probability at time t, the busy period, and the number of customers at time t given that m customers have left the system at time t since the commencement of the current busy period. The virtual waiting time at time t is also analyzed. Closed form solutions are derived for the case that Vk are i.i.d., for k ≧ 2.
