This paper analyzes a discrete-time, finite capacity, deterministic service time queueing system (MMBP + Ml\!fBP(XljD(N)jljK) with superposing non-renewal arrival processes. This queueing system models a switch in high speed networks, where multiple applications which generate correlated and bursty traffic are supported simultaneously using fast packet switching. A designated arrival stream (VC...

Dynamic mapping (matching and scheduling) heuristics for a class of independent tasks using heterogeneous distributed computing systems are studied. Two types of mapping heuristics are considered: immediate mode and batch mode heuristics. Three new heuristics, one for batch mode and two for immediate mode, are introduced as part of this research. Simulation studies are performed to compare thes...

Spectral lag, which is defined as the difference in time of arrival of high and low energy photons, is a common feature in Gamma-ray Bursts (GRBs). Previous investigations have shown a correlation between this lag and the isotropic peak luminosity for long duration bursts. However, most of the previous investigations used lags extracted in the observer-frame only. In this work (based on a sampl...

It is shown that a Markovian queue, with bulk arrivals and departures having any probability mass functions for their batch sizes, has geometrically distributed queue length at equilibrium (when this exists) provided there is an additional special bulk arrival stream, with particular rate and batch size distribution, when the server is idle. It is shown that the time-averaged input rate of the ...

We consider a single-server priority queue with batch arrivals. We treat the head-of-the-line (HL) or preemptive-resume (PR) priority rule. Assuming that the arrival process of batches is renewal for each priority class and using the point process approach, we express the individual class queue-length distribution in terms of the waiting time and the completion time distributions. Assuming furt...

Abstract: We propose new approximate formulas for the distribution functions of the delay in batch arrival M/G/1 nonpreemptive and preemptive resume priority queues. It is assumed that the delay consists of the waiting time and the service time of a whole batch. Our formulas are of the exponential distribution type with the coefficients being matched with the exact mean and second moment of the...

We consider an online scheduling problem in a parallel batch processing system with jobs in a batch being allowed to restart. Online means that jobs arrive over time, and all jobs’ characteristics are unknown before their arrival times. A parallel batch processing machine can handle up to several jobs simultaneously. All jobs in a batch start and complete at the same time. The processing time o...

We study a simple network with two parallel batch service queues, where service at a queue commences when the batch is full and each queue is served by infinitely many servers. A stream of general arrivals observe the current state of the system on arrival and choose which queue to join to minimize their own expected transit time. We show that for each set of parameter values there exists a uni...