We consider an M/G/1 quening system, where batches of customers are assumed to arrive the system according to a compound Poisson process. As soon as the system becomes empty, the server takes a vacation for a random length of time called vacation time to do other jobs, which is uninterruptible. After returning from that vacation, there are two possibilities viz. (i) he keeps on taking vacations...

In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of D queues, in a system of N queues; after completion of service at its queue, a job leaves the network. We also assume that jobs arrive into the system according to a rate-αN Poisson process, α < 1, with rate1 service at each queue. When the service at queues is exponentia...

We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite buffer (M/G/1/n) systems. We show the somewhat surprising result that for three variations of the preemptive LCFS discipline, the maximum queue ...

We study the impact of service time distributions on the distribution ofthe maximum queue length during a busy period for the Mx/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come-first-served discipline,...

To better understand how to interpret birth-and-death (BD) processes fit to service system data, we investigate the consequences of fitting a BD process to a multi-server queue with a periodic time-varying arrival rate function. We study how this fitted BD process is related to the original queue-length process. If a BD process is fit to a segment of the sample path of the queue-length process,...

We consider a finite buffer queue with one deterministic server fed by packets arriving in batches. We assume that we are not able to fully describe the batch distribution: only the maximal size and the average number of packets are supposed known. Indeed, these two quantities are simple to measure in a real system. We additionally allow the batch distribution to be state dependent. We analyze ...

We derive asymptotic expressions for the distribution of the total queue length in a polling model with two classes of customers and unequal service rates. The server employs a scheduling policy that alternately visits each queue, with the maximum number served in each visit potentially being different for each queue. We provide sufficient conditions for the behaviour to lie in one of two regim...

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obta...

Active queue management schemes like RED (Random Early Detection) have been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows and packets are lost. When the queue length reaches a certain threshold RED schemes drop/mark incoming packets with a probability that increases as the queue size increases. The ...