Internet usage has been integrated into most of our activities because of the convenience and accessibility it offers. Arguably, the most common holiday-related online activity users engage in is shopping. Each year, online shoppers troop online to search for the latest promos, coolest gifts, and biggest bargains or to book flights and reservations to go on their dream vacations during the Chri...

This report presents a method for analyzing a queueing model with repeated inhomogeneous vacations. At the end of a vacation, the server goes on another vacation, possibly with a different probability distribution, if during the previous vacation there have been no arrivals. In order to get an insight on the influence of parameters on the performance, we choose to study a simple M/G/1 queue (Po...

We consider the busy period in the GI/M/1 queue with multiple exponential vacations. We derive the transform of the joint distribution of the length of a busy period, the number of customers served during the busy period, and the residual interarrival time at the instant the busy period ends.

Consider an M/M/1 queueing system with server vacations where the server is turned oo as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding co...