Xq. Tan et Cr. Knessl, INTEGRAL-REPRESENTATIONS AND ASYMPTOTICS FOR INFINITE-CAPACITY AND FINITE-CAPACITY QUEUES DESCRIBED BY THE UNFINISHED WORK .2., SIAM journal on applied mathematics, 57(3), 1997, pp. 824-870
We continue our study of a finite-capacity queue with customer loss. W
e construct asymptotic expansions for the transient probability distri
bution of the unfinished work. It is assumed that the system's capacit
y of unfinished work is large. We consider all possible initial condit
ions and several cases of the model parameters. We also give asymptoti
c approximations for the rate at which customers are lost. The results
are obtained by using integral representations and the saddle point m
eshed.