The MVA Priority Approximation

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation

The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in Stochastic Model

Spare parts provisioning for multiple k-out-of-n:G systems

In this paper, we consider a repair shop that fixes failed components from different k-out-of-n:G systems. We assume that each system consists of the same type of component; to increase availability, a certain number of components are stocked as spare parts. We permit a shared inventory serving all systems and/or reserved inventories for each system; we call this a hybrid model. Additionally, we consider two alternative dispatching rules for the repaired component. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our analysis gives the steady-state system size distribution of the two alternative models at the repair shop. We conduct numerical examples minimizing the spare parts held while subjecting the availability of each system to exceed a targeted value. Our findings show that unless the availabilities of systems are close, the HP policy is better than the HF policy

An Introduction to the RESearch Queueing Package for Modeling Computer Systems and Communication Networks

A queueing network is an important tool for modeling systems where performance is principally affected by contention for resources. Such systems include computer systems, communication networks and manufacturing lines. In order to effectively use queuing networks as performance models, appropriate software is necessary for definition ofthe networks to be solved, for solution ofthe networks and for examination of the performance measures obtained. The RESearch Queueing Package (RESQ) and the RESearch Queueing Package Modeling Environment (RESQME) form a system for constructing, solving and analyzing extended queueing network models. We refer to the class of RESQ networks as extended because of characteristics which allow effective representation of system detail. RESQ incorporates a high level language to concisely describe the structure of the model and to specify constraints on the solution. A main feature of the language is the capability to describe models in a hierarchical fashion, allowing an analyst to define submodels to be used analogously to use of macros in programming languages. RESQ also provides a variety of methods for estimating the accuracy of simulation results and for determining simulation run lengths. RESQME is a graphical interface for RESQ. In this introduction, we limit our examples to computer systems and communication networks. Acknowledgement: The authors wish to thank their co-developers of RESQME: Jim Kurose and Kurt Gordon. We also want to thank Ben Antanaitis, Howard Jachter, Jack Servier, Daniel Souday and Peter Welch for their many suggestions which helped improve the RESQME package and Anil Aggarwal, Al Blum, Gary Burkland, Rocky Chang, Janet Chen, Diana Coles, Prakash Deka, Paul Lnewner, and Geoff Parker for their work in implementing RESQME. We would also like to thank our users for their ideas and feedback that we tried to incorporate in RESQ and RESQME. We remain indebted to Charlie Sauer for his design, guidance, inspiration, and development ofthe RESQ languag

A Simple, Practical Prioritization Scheme for a Job Shop Processing Multiple Job Types

The maintenance, repair, and overhaul (MRO) process is used to recondition equipment in the railroad, off-shore drilling, aircraft, and shipping industries. In the typical MRO process, the equipment is disassembled into component parts and these parts are routed to back-shops for repair. Repaired parts are returned for reassembling the equipment. Scheduling the back-shop for smooth flow often requires prioritizing the repair of component parts from different original assemblies at different machines. To enable such prioritization, we model the back-shop as a multi-class queueing network with a ConWIP execution system and introduce a new priority scheme to maximize the system performance. In this scheme, we identify the bottleneck machine based on overall workload and classify machines into two categories: the bottleneck machine and the non-bottleneck machine(s). Assemblies with the lowest cycle time receive the highest priority on the bottleneck machine and the lowest priority on non-bottleneck machine(s). Our experimental results show that this priority scheme increases the system performance by lowering the average cycle times without adversely impacting the total throughput. The contribution of this thesis consists primarily of three parts. First, we develop a simple priority scheme for multi-class, multi-server, ConWIP queueing systems with the disassembly/reassembly feature so that schedulers for a job-shop environment would be able to know which part should be given priority, in what order and where. Next, we provide an exact analytical solution to a two-class, two-server closed queueing model with mixed non-preemptive priority scheme. The queueing network model we study has not been analyzed in the literature, and there are no existing models that address the underlying problem of deciding prioritization by job types to maximize the system performance. Finally, we explore conditions under which the non-preemptive priority discipline can be approximated by a preemptive priority discipline