The primary aim of this paper is to answer the question: what are the highest-order fiveor nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the oneand two-dimensional Poisson equation on uniform, quasi-uniform, and non-uniform face-to-face hyper-rectangular grids and directly prove the existence or non-...

The model is a service system, consisting of several large server pools. A server processing speed and buffer size (which may be finite or infinite) depend on the pool. The input flow of customers is split equally among a fixed number of routers, which must assign customers to the servers immediately upon arrival. We consider an asymptotic regime in which the customer total arrival rate and poo...

Vacation time queues with Markovian arrival process (MAP) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a single-server finite capacity queue wherein service is performed in batches of maximum size “b” with a minimum threshold “a” and arrivals are governed by MAP. The server takes a...

This paper develops a finite-capacity single-vacation queueing model with close-down/setup times and batch Markovian arrival process (BMAP) for the statistic behavior of the typical ARQ schemes (Stop-and-Wait, Go-Back-N, Selective Repeat) at transmitter buffer. We obtain the queue length distribution, the average waiting time of arbitrary data frame and the server utilization ratio of the trans...

The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing system where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity properties under the assumptions of a single-server and constant batch sizes. Even though our proof c...

In this paper we study the asymptotic relationship between the loss ratio in a finite buffer system and the overflow probability (the tail of the queue length distribution) in the corresponding infinite buffer system. We model the system by a fluid queue which consists of a server with constant rate c and a fluid input. We provide asymptotic upper and lower bounds on the difference between log ...

A statistical multiplexer is a basic model used in the design and the dimensioning of communication networks. The multiplexer model consists of a finite buffer, to store incoming packets, served by a single server with constant service time, and a more or less complicated arrival process. The aim is to determine the packet loss probability as a function of the capacity of the buffer. An exact a...

In this paper we examine the queuing behavior of a multi-stage multiplexer with fixed length packets flowing through the stages. The system consists of two components: a front end multi-input, multi-output device as a preliminary stage, and a single-server, deterministic service time queue system (multiplexer) as a final stage. We treat arbitrary exogenous arrival patterns and examine sample pa...

OPTIMAL TOPOLOGICAL ARRANGEMENTS OF QUEUES IN CLOSED FINITE QUEUEING NETWORKS MAY 2015 LENING WANG M.S.M.E., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor J. MacGregor Smith Closed queueing networks are widely used in many different kinds of scientific and business applications. Since the demands of saving energy and reducing costs are becoming more and more significant with develo...

This paper continues to study the problem of optimally admitting a finite number customers from an auxiliary buffer with a low holding cost into a single–server queue with a high holding cost without observing the status of the single-server queue, which was introduced in Part I. This paper first proves a few asymptotic properties of the sequence of optimal schedules indexed by the number of cu...