In this paper, the queue occupancy distribution of the DQDB station is derived through the formulation and exact analysis of a queueing model with the following characteristic: the packet service time requirement depends on the state of an underlying Markov-structured process at the time when the packet is forwarded to the server (head of the queue). Numerical results are presented and compared...

This paper analyses a single server with bulk service queue with general arrival pattern and multiple working vacation period. The model is analyzed by using Embedded Markov Chain technique. The steady state probability distribution at pre arrival epoch and arbitrary epoch are derived and measures like mean queue length are calculated. Finally, through some numerical examples, the parametric ef...

Previously, we derived the two-dimensional transforms of the emptiness function, the transient workload and queue-length distributions in the single-server queue with general service times and a batch Markovian arrival process (BMAP). This arrival process includes the familiar phase-type renewal process and the Markov modulated Poisson process as special cases, as well as superpositions of thes...

On the basis of establishing mathematical model and defining the parameters and treating embedded Markov chains and probability generating function as math tools, the paper analyzed discrete-time, nonsymmetric dual-threshold service queue system precisely, and it derived first order and second order characteristics of the system. The paper calculates the average queue length and average waiting...

We analyze a priority queueing system with congestion control based on thresholds. A priority queue with a triple of thresholds consisting of an abatement threshold, an onset threshold and a discard threshold was investigated by San-qi Li. We extend Li's model to a priority queue with N triples of thresholds and obtain the stationary probabilities of queue length by using the Embedded Markov ch...

This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue length...

We consider the single server, finite capacity queue with Poisson arrivals and generally distributed service times. The M/G/1/K system may be analysed using an imbedded Markov Chain approach very similar to the one followed in Section 3.2. A queue of this type may be a better representation of a real-life system. This is because the infinite number of buffers implied by the M/G/1 (really the M/...

In this paper, we discuss the discrete-time Geom/G/1 queue with multiple adaptive vacations and server setup/closedown times. We consider two types of closedown time policies which differ from each other in the completion instant of the closedown times and contrast the effects of them on the queueing system. We derive the probability generating functions (PGFs) and stochastic decomposition resu...

In this paper, we refine the calculus proposed in [5, 8, 91. The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or auto...