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

Analysis of a queuing model for slotted ring networks

We study a multi-server multi-queue system which is intended to model a local area network with slotted ring protocol. Two special cases of the model are analysed and the results are used to motivate an approach to approximate mean queue lengths in the general model

Analysis of Multiple Flows using Different High Speed TCP protocols on a General Network

We develop analytical tools for performance analysis of multiple TCP flows (which could be using TCP CUBIC, TCP Compound, TCP New Reno) passing through a multi-hop network. We first compute average window size for a single TCP connection (using CUBIC or Compound TCP) under random losses. We then consider two techniques to compute steady state throughput for different TCP flows in a multi-hop network. In the first technique, we approximate the queues as M/G/1 queues. In the second technique, we use an optimization program whose solution approximates the steady state throughput of the different flows. Our results match well with ns2 simulations.Comment: Submitted to Performance Evaluatio

Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

Modelling network memory servers with parallel processors, break-downs and repairs.

This paper presents an analytical method for the performability evaluation of a previously reported network memory server attached to a local area network. To increase the performance and availability of the proposed system, an additional server is added to the system. Such systems are prone to failures. With this in mind, a mathematical model has been developed to analyse the performability of the proposed system with break-downs and repairs. Mean queue lengths and the probability of job losses for the LAN feeding the network memory server is calculated and presented

Modeling Stochastic Lead Times in Multi-Echelon Systems

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained

Closed-loop two-echelon repairable item systems

In this paper we consider closed loop two-echelon repairable item systems with repair facilities both at a number of local service centers (called bases) and at a central location (the depot). The goal of the system is to maintain a number of production facilities (one at each base) in optimal operational condition. Each production facility consists of a number of identical machines which may fail incidentally. Each repair facility may be considered to be a multi-server station, while any transport from the depot to the bases is modeled as an ample server. At all bases as well as at the depot, ready-for-use spare parts (machines) are kept in stock. Once a machine in the production cell of a certain base fails, it is replaced by a ready-for-use machine from that base's stock, if available. The failed machine is either repaired at the base or repaired at the central repair facility. In the case of local repair, the machine is added to the local spare parts stock as a ready-for-use machine after repair. If a repair at the depot is needed, the base orders a machine from the central spare parts stock to replenish its local stock, while the failed machine is added to the central stock after repair. Orders are satisfied on a first-come-first-served basis while any requirement that cannot be satisfied immediately either at the bases or at the depot is backlogged. In case of a backlog at a certain base, that base's production cell performs worse. To determine the steady state probabilities of the system, we develop a slightly aggregated system model and propose a special near-product-form solution that provides excellent approximations of relevant performance measures. The depot repair shop is modeled as a server with state-dependent service rates, of which the parameters follow from an application of Norton's theorem for Closed Queuing Networks. A special adaptation to a general Multi-Class MDA algorithm is proposed, on which the approximations are based. All relevant performance measures can be calculated with errors which are generally less than one percent, when compared to simulation results. \u