In this paper we analyze the average queue lengths in a combined input-output queued switch using a maximal size matching scheduling algorithm. We compare these average queue lengths to the average queue lengths achieved by an optimal switch. We model the cell arrival process as independent and identically distributed between time slots and uniformly distributed among input and output ports. Fo...

In this paper, we study N-policy for a finite population Bernoulli feedback queueing model for machine repair problem with degraded failure. The running times of the machines between breakdowns have an exponential distribution. The repair times of the machines are independent and identically distributed random variables. If at any time a machine fails, it is sent to the repairman for repairing,...

We explore the performance of an M/GI/1 queue under various scheduling policies from the perspective of a new metric: the slowdown experienced by largest jobs. We consider scheduling policies that bias against large jobs, towards large jobs, and those that are fair, e.g., Processor-Sharing. We prove that as job size increases to infinity, all work conserving policies converge almost surely with...

We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and the service time of each individual customer is drawn from a general probability distribution function. Thus, each of the queues comprising the system is, in isolation, an M/G...

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...

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability (1−b). We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heter...

We derive an integral equation for the transient probabilities and expected number in the queue for the multiserver queue with Poisson arrivals, exponential service for timevarying arrival and departure rates, and a time-varying number of servers. The method is a straightforward application of generating functions. We can express pĉ−1(t), the probability that ĉ − 1 customers are in the queue or...

We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and service time of each individual customer is drawn from a general probability distribution function. Thus, each of the queues comprising the system is, in isolation, an M/G/∞-t...

Active queue management policies and in particular Random Early Detection RED are being advocated by the Internet Engineering Task Force IETF as additional mechanisms in Internet routers to control congestion and keep network utilization high RED s performance is highly dependent on the settings of its ve control parameters However no rm guidelines exist on con guring RED parameters and the cur...