This paper considers queues with server vacations, but departs from the traditional setting in two ways: (i) the queueing model is driven by Lévy processes rather than just compound Poisson processes; (ii) the vacation lengths depend on the length of the server’s preceding busy period. Regarding the former point: the Lévy process active during the busy period is assumed to have no negative jump...

This paper considers a stable GI|GI|1 queue with a regularly varying service time distribution. We derive the tail behaviour of the integral of the queue length process Q(t) over the busy period. We show that an occurrence of a large integral is related to an occurrence of a large maximum of the queueing process over the busy period and we exploit asymptotic result for this variable. We also pr...

Larson [1] proposed a method to statistically infer the expected transient queue length during a busy period in 0(n 5) solely from the n starting and stopping times of each customer's service during the busy period and assuming the arrival distribution is Poisson. We develop a new O(n 3) algorithm which uses this data to deduce transient queue lengths as well as the waiting times of each custom...

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...