The principle of maximum entropy (ME) is used to analyse a stable G/G/c/PR queue with general interarrivai and service times, c (> 2) parallel servers and R (> 2) priority classes under preemptive resume (PR) scheduling. The form of the joint state probability is characterised, subject to the existence of constraint information involving normalisation, marginal mean queue lengths and the probabilities of having a least number j of busy servers with jobs of class r. For R = 2, new closed-form approximations for the marginal state probabilities (per class), as explicit functions of the above constraints, are derived. Moreover, these ME solutions are also applied, in conjunction with the method of class aggregation, to the case of an arbitrary number of classes R (> 2). To illustrate the utility of the ME solutions the Generalised Exponential (GE) model is used to approximate general distributions with known first two moments, and exact as well as approximate stochastic analysis is carried out for estimating the associated constraints of interest. Numerical examples illustrate the accuracy of the proposed approximations in relation to simulations involving different interarrivai and service time distributions per class. Concluding remarks and comments on the extension of the work to the analysis of general queueing networks are included.
This paper reports on a trial application of the Process Interaction modelling tool, PIT, to a class of problems in the area of broadband communication networks. The activity forms part of the Esprit-II project 2143 to develop an Integrated Modelling Support Environment. The specific application was provided by the ATMOSPHERIC project of the RACE programme and is fo-cussed on the modelling of two components: a service access switch and a link multiplexor. In each case the structural details and functionality were kept to a minimum, and attention was directed to modelling the congestion effects of mixed traffic types.
A perspective is offered for viewing the history, and projecting the future, of tools and environments for performance analysis. This is derived by attempting to capture performance analysis as a process and then considering how this process may be supported efficiently from the user point of view. It is argued that such a conceptual modelling approach will enable developers to minimise the load on users in making use of the wide and growing range of tools and techniques on offer.
We derive an approximate algorithm to predict the mean transmission time through finitely buffered, packet-switched, asynchronous networks with no feedback. We tailor the algorithm to banyan networks, which are important in parallel computer architectures and telecommunication systems, and present preliminary numerical results. The full paper appears in [3].
This paper will show how to solve simple closed queueing network models using spreadsheets. Over the past decade there has been a growth in the use of personal computers and spreadsheets on the one hand and a growth in the use of approximate solution methods on the other. This paper will show that it is possible to use spreadsheets to re-create well known fixed point or approximate Mean Value Analysis results.
We consider a time-sharing model with a single server, multiple queues, priorities, and feedback to lower priority queues, which, disregarding the service discipline, is of type M/G/l. In the model, there is a finite or countably infinite number K of queues. Jobs arrive at queue 1 according to a Poisson process. A fraction qk+1 of jobs is appended to queue k + 1 after having received service in queue k; the remainder leaves the system. Feedback may or may not depend on service time. Jobs in queue k have priority over jobs in queue /, when k < I. In [7], Schräge introduces a method to derive the Laplace-Stieltjes transform of the total residence time in queues 1,2,..., j of jobs that ever reach queue j, and Wolff [9] uses the same method to derive the total delay in queues 1,2,..., j in the special case of one overall service time and quantum allocation, both in the nonpreemptive case. In this paper, this method is extended to the preemptive discipline, and analogous results are obtained.
Queueing network solution packages that analyse the performance of BCMP networks are widely available, and are one of the standard tools of the performance analyst. Stochastic Petri net analysis packages are less commonly used. They have only recently emerged from the research laboratory, and are not in widespread commercial use. This paper takes a particular problem, diskless workstation configuration management, and analyses it using tools of both types. Although the theoretical limitations of both types of solution package are well known, little work has been done to compare their practical performance.
The access protocols for computer communication networks can, in principle, be modelled as multidimensional Markov chains. In most practical systems however, the state-space is so vast that a solution by classical Markov analysis is intractable, and some approximation technique must be used. In this paper the access protocol of a slotted ring network is modelled as a discrete-time Markov chain, and its solution is obtained by equilibrium point analysis (EPA), a method that approximates the stationary probability distribution of the Markov chain by a unit impulse located at a point in the state-space where the system is in equilibrium. The model is found to give good results over a wide range of parameter values when compared with an equivalent simulation study.
The Maximum Entropy Method (MEM) is used to approximate the joint stationary queue length distribution of an M/M/1/N queueing system with finite capacity, iV, R(R > 1) classes of jobs under an unrestricted buffer sharing scheme and mixed service disciplines drawn from FCFS, LCFS-NPR, LCFS-PR and PS rules. The marginal and aggregate ME queue length distributions and the associate blocking probabilities per class are also determined. These ME results in conjunction with the first moment of the effective flow are used, as building blocks, in order to establish a new product-form approximation for arbitrary exponential multi-class open queueing networks under repetitive-service (RS) blocking with random destination (RD). Numerical experiments illustrate the credibility of the ME approximations in relation to simulation.
We wish to be able to predict the execution time of a parallel program from a knowledge of the values of certain parameters of the program and the environment in which it runs, and in order to do this, we have to discover which factors have an important influence on performance. In this paper, we describe a methodology for constructing synthetic programs corresponding to a particular model of parallel computation, simulating their execution, and analysing performance data using standard statistical techniques to estimate effects due to the various factors. The method is applied to a model representing parallel programs consisting of uniform concurrent processes, to show the kind of quantitative information that can be derived from experiments of this type
The Concatenated LOcal-area and Wide-area Network simulator is a highly modular simulation environment. In its current form, it has been developed to accelerate the performance analysis of a wide range of communication problems. Its window based user interface and macro building facilities simplifies the model building process, and its interactive facilities makes it very suitable for the study of finite horizon problems.
This paper describes ongoing work in FDDI performance evaluation by means of an emulator. The emulator is part of an experimental system being used to investigate integration of multimedia traffic at the interface between a workstation and a multiservice network. Emulation is being used to evaluate the suitability of a number of emerging high speed networks as carriers of this type of traffic. A detailed description of one particular emulation, that of an FDDI network, is given in this paper followed by some preliminary performance results. Finally the future direction of the emulation work is outlined.
A significant computational gain can be achieved through concurrent programming by exploiting parallel and distributed processing capabilities of current computer system architectures. The performance evaluation and quantitative analysis of such systems have become important due to the multiplicity of the component parts and the complexity of their functioning. In this paper an approximate method is developed for the analysis of general queueing network models of computer systems with variable concurrency and synchronisation structures. It is based on the maximum entropy algorithm and the notion of surrogate delays. Numerical examples illustrate the capability of the proposed algorithm in comparison to simulation.
This paper considers performance prediction for various computer networks in terms of the number of references made to the memory. Analytical solutions were obtained for the models with multiple requests to the memory and parallel access to one memory bank with a Negative Exponential distribution of requests generated by CPUs. Numerical simulation was carried out for Hyper-cube, Cube Connected Cycle and Torus processor networks. The distributed parallel architectures investigated could be viewed as PRAM simulating models. The analytical solutions are compared to numerical simulation results.
As a first step towards providing automatic compile- and run-time process allocation decisions for distributed memory multiprocessors we are investigating appropriate performance models for various classes of message passing parallel programs. This paper describes a modelling environment within which experiments concerning the behaviour of message passing parallel programs can be carried out.
