Tan, Xiaoqian; Knessl, Charles; Yang, Yongzhi - In: Stochastic Processes and their Applications 123 (2013) 6, pp. 2175-2227
We consider the finite capacity M/M/1−K queue with a time dependent arrival rate λ(t). Assuming that the capacity K is large and that the arrival rate varies slowly with time (as t/K), we construct asymptotic approximations to the probability of finding n customers in the system at time t, as...