— We consider in this paper the steady state behaviour of a Queueing System with queue length dependent additional server facility wherein arrivais occur in batches of variable size. Whenever the queue length in front of the first server reaches a certain lenght, the system adds another server. Steady state probabilities and expected queue lengths in Single Server System and Additional Server S...

In this article we study the maximum queue length M in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy tailed) service time distributions the Foreground Background service discipline is optimal. This discipline gives service to those customer(s) that have received the least amount of service so far. It will be shown that under this discip...

There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where 0 < λ < 1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate...

A general framework is developed for analyzing a wide class of vehicle dispatching strategies for bulk arrival, bulk service queues. A simple derivation of the queue length transform for the imbedded Markov chain is provided and a new computational procedure is developed for finding the moments of the queue length distribution. Extensive computational tests are reported which demonstrate that t...

In this paper, it is studied about finite buffer bulk service queue M/G (a,b) /1 with multiple vacations and some analytical results, relations among queue length distributions, computations of state probabilities at various epochs are included.

to be constant and the input and output flows reach equilibrium (2, 10). Further improvement includes providing queue length in small time stamps on the basis of vehicle arrival and departure profiles, first applied in the software TRANSYT (11). This approach was later extended and named the incremental queue accumulation method (12, 13). Stochastic analysis is also introduced to address the st...

For the case of HME-based controllers, we see that queue length increases to a large peak at the initial stage, followed by a transient period of less than optimum link utilisation. This corresponds to the period before HME has learnt, because we h a ve used random initial weights for the HME. In actual applications, the combination of both on-line and o-line training may be necessary. The init...

In this paper, we consider a discrete-time finite-buffer queue with correlated arrivals and service interruptions and the corresponding infinite-buffer queue. Under some assumptions, we derive an exact relation holding between the loss probability in the finite-buffer queue and the queue length distribution in the corresponding infinite-buffer queue. The exact relation is considered as an integ...