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...

Example 1 Consider a queue where customers arrive one by one. There is a single server that serves each customer on a first-come-first-served basis. Define the sojourn time experienced by a customer as the time he/she spends in the system: waiting (if any) for service plus the duration of the service at the server. The server toggles between being idle for some time when there are no customers ...

The multi-server systems with dynamic routing protocol were investigated in a number of papers, see for example [1]-[9], in particular different asymptotic properties of such systems were investigated. Consider a system S with k servers {si}, i = 1, ..., k, and ` input Poisson flows {fj}, j = 1, ..., `, of intensity λj. Each flow is assigned to some subgroup Sj of mj, servers sj1 , ..., sjmj , ...

Analysis of Idle and busy period of any communication system gives the overall information about system behavior when system is empty and data present in the system. In this paper we use a queueing theory approach to model the system with two class data traffic. we develop and analyze the idle and busy period of two class data traffic through queueing system using Markov chain. We also develop ...

There are many apparent reasons why people engage in activity, such as to earn money, to become famous, or to advance science. In this report, however, we suggest a potentially deeper reason: People dread idleness, yet they need a reason to be busy. Accordingly, we show in two experiments that without a justification, people choose to be idle; that even a specious justification can motivate peo...