Queueing systems in which an arriving job is blocked and lost with a probability that depends on the queue size are studied. The study is motivated by the popularity of Active Queue Management (AQM) algorithms proposed for packet queueing in Internet routers. AQM algorithms often exploit the idea of queue-size based packet dropping. The main results include analytical solutions for queue size d...

In this paper, we analyze a bulk input Geom/Geom/1 queue with single working vacation. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived, from which we got the stochastic decomposition result for the PGF of the stationary queue size. It is important that we find the biparameter addition theorems of the conditional negative binomial distribu...

This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization principle.

In this paper we study a single-server queue with FIFO service and cyclic interarrival and service times. An efficient approximative algorithm is developed for the first two moments of the waiting time. Numerical results are included to demonstrate that the algorithm yields accurate results. For the special case of exponential interarrival times we present a simple exact analysis.

We describe a scalable priority queue manager that implements deadline-ordered service disciplines in an output-buffered ATM switch, which can be used as a switching node in high-speed packet switched networks to provide quality of service (QoS) guarantees. The priority queue manager can handle a range of priority levels from to , a buffer size of 64K ATM cells, and 16 input links at 2.5 Gb/s. ...

Closed product-form queueing networks are considered. Mean value analysis is further developed to become "moment analysis", a recursive evaluation schema for moments of the queue lengths and customers' sojourn times at FCFS centers. As with mean value analysis, in general no state probabilities are needed. Moment analysis can be approximately done by an extended Linearizer algorithm.

We consider the dispatching problem in a sizeand state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By sizeand state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on min...

In this paper, an infinite-buffer fluid queue driven by an M/G/1 queue is discussed. The Laplace transform of the distribution of the stationary buffer content is expressed through the minimal positive solution to a crucial equation, similar to the fundamental equation satisfied by the busy period of an M/G/1 queue. Furthermore, the distribution of the stationary buffer content is shown to be r...

An alternative simple approach to Takâcs [8] procedure , which appears to economize in algebra is given. It is also shown that the measures of effectiveness such as the first and second order moments of the queue length can be easily obtained in a elegant closed form.