Queues with setup time are extensively studied because they have application in performance evaluation of power-saving data centers. In a data center, there are a huge number of servers which consume a large amount of energy. In the current technology, an idle server still consumes about 60% of its peak processing a job. Thus, the only way to save energy is to turn off servers which are not pro...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discreteMarkovian service process. The server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is N. We obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary...

 This paper deals with batch arrival unreliable queue with two phases of service and vacation under Bernoulli vacation schedule, which consist of a breakdown period and a delay period. For this model, we first derive the joint distribution of state of the server and queue size, which is one of the chief objectives of this paper. Secondly, we derive the pgf of the stationary queue size distribu...

This paper introduces the procedure for an analytical derivation of the drop probability function for the Random Early Detection queue management mechanism. The procedure is based on a model of the TCP window system and the establishment for a criterion for system stability with methods of control theory. The term stability refers to the oscillation amplitude of the steady state queue size. The...

In this paper, we present a randomized algorithm for the multipacket (i.e., k − k) routing problem on an n × n mesh. The algorithm completes with high probability in at the most kn + O(k logn) parallel communication steps, with a constant queue size of O(k). The previous best known algorithm [3] takes 5 4kn + O( kn f(n) ) steps with a queue size of O(k f(n)) (for any 1 ≤ f(n) ≤ n). We will also...

The Gauss hypergeometric distribution with the density proportional to xα−1 (1− x)β−1 (1 + ξx)−γ , 0 < x < 1 arises in connection with the priori distribution of the parameter ρ (0 < ρ < 1) representing traffic intensity in a M/M/1 queue system. In this article, we define and study a multivariate generalization of this distribution and derive some of its properties like marginal densities, join...

We consider a queueing system with disruptive and non-disruptive server interruptions. Both disruptive and non-disruptive interruptions may start when there is a customer in service. The customer repeats its service after a disruptive interruption, and continues its service after a nondisruptive interruption. Using a transform approach, we obtain various performance measures such as the moments...

The focus of this work is to study the behaviors of varies queue managements, including RED (Random Early Detection), SRED (Stabilized-RED), and BLUE. The performance metrics of the comparison are queue size, the drop probability, and link utilization. The simulation is done using NS-2. The results of this work shows that different from the RED, SRED and BLUE, which use the available queue leng...

The Internet routers employing the random early detection (RED) algorithm for congestion control suffer from the problem of chaotic queue oscillation. It is well known that the slowly varying nature of the average queue size computed using an exponentially weighted moving average (EWMA) used in the RED scheme causes this chaotic behavior. This paper presents a new mathematical function to model...