Gerald S. Shedler

An anomaly in space-time characteristics of certain programs running in a paging machine

The running time of programs in a paging machine generally increases as the store in which programs are constrained to run decreases. Experiment, however, have revealed cases in which the reverse is true: a decrease in the size of the store is accompanied by a decrease in running time. An informal discussion of the anomalous behavior is given, and for the case of the FIFO replacement algorithm a formal treatment is presented.

Regenerative Simulation of Response Times in Networks of Queues

1.0 Introduction.- 2.0 Simulation of regenerative processes.- 3.0 Closed networks of queues.- 4.0 The marked job method.- 5.0 Examples and simulation results.- 6.0 Finite capacity open networks of queues.- 7.0 Marked job simulation via hitting times.- 8.0 The decomposition method.- 9.0 Efficiency of simulation.- 10.0 Networks with multiple job types.- 11.0 Implementation considerations.

Statistical analysis of non-stationary series of events in a data base system

Central problems in the performance evaluation of computer systems are the description of the behavior of the system and characterization of the workload. One approach to these problems comprises the interactive combination of data-analytic procedures with probability modeling. This paper describes methods, both old and new, for the statistical analysis of non-stationary univariate stochastic point processes and sequences of positive random variables. Such processes arefr equently encountered in computer systems. As an illustration of the methodology an analysis is given of the stochastic point process of transactions initiated in a running data base system. On theb asis of the statistical analysis, a non-homogeneous Poissonp rocess model for the transaction initiation process is postulated for periods of high system activity and found to be an adequate characterization of the data. For periods of lower system activity, the transaction initiation process has a complex structure, with more clustering evident. Overall models of this type have application to the validation of proposed data base subsystem models.

Processor Utilization in Multiprogramming Systems via Diffusion Approximations

Cyclic queuing systems have been proposed by several authors in the study of the behavior of multiprogrammed computer systems. Programs in the system wait for service at the central processor unit CPU; then, after page fault or input-output request at a data transmission unit DTU, the process repeats until the program completes. Semi-Markov analysis of such systems, based on the apparently plausible assumption of independently but exponentially distributed CPU burst time, and independent, but nearly constant DTU tune may be conducted. This paper presents some very simple approximations based on a continuous-state approximation-the simple diffusion with two reflecting barriers-to describe the CPU utilization. Computational experience from which the quality of the approximations can be assessed is reported.

Numerical analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions

This paper introduces an efficient numerical algorithm for transient analysis of deterministic and stochastic Petri nets (DSPNs) and other discrete-event stochastic systems with exponential and deterministic events. The proposed approach is based on the analysis of a general state space Markov chain (GSSMC) whose state equations constitute a system of multidimensional Fredholm integral equations. Key contributions of this paper constitute the observations that the transition kernel of this system of Fredholm equations is piece-wise continuous and separable. Due to the exploitation of these properties, the GSSMC approach shows great promise for being effectively applicable for the transient analysis of large DSPNs with concurrent deterministic transitions. Moreover, for DSPNs without concurrent deterministic transitions the proposed GSSMC approach requires three orders of magnitude less computational effort than the previously known approach based on the method of supplementary variables.

Stochastic Petri net representation of discrete event simulations

In the context of discrete event simulation, the marking of a stochastic Petri net (SPN) corresponds to the state of the underlying stochastic process of the simulation and the firing of a transition corresponds to the occurrence of an event. A study is made of the modeling power of SPNs with timed and immediate transitions, showing that such Petri nets provide a general framework for simulation. The principle result is that for any (finite or) countable state GSMP (generalized semi-Markov process) there exists an SPN having a marking process that mimics the GSMP in the sense that the two processes (and their underlying general state-space Markov chains) have the same finite dimensional distributions. >

Regenerative generalized semi-markov processes

A generalized semi-Markov process (GSMP) is the usual model for a discrete event simulation. The standard formulation assumes that the current state of the process uniquely determines the set of events that are scheduled to occur and that the state transition probabilities depend only on the current state, the next state, and the trigger event. We provide a formulation of a GSMP that avoids these restrictions, thus permitting formal specification of many non-Markovian simulation models. Using a monotone replacement property of “new better than used” distributions and sample path properties of the GSMP, we provide a criterion for recurrence in this setting and conditions under which a GSMP is a regenerative process and the time between regeneration points has finite moments. Steady state estimation methods for non-Markovian stochastic network simulations follow.

Approximate Models for Processor Utilization in Multiprogrammed Computer Systems

This paper presents results of an approximation study of cyclic queueing phenomena that occur in multiprogrammed computer systems. Based on Wald’s identity and using ideas of diffusion, the objective is to develop convenient and nearly explicit formulas relating processor utilization in such systems to simple program parameters and the level of multiprogramming. Some numerical results to indicate the quality of the proposed approximation are given.

A Cyclic-Queue Model of System Overhead in Multiprogrammed Computer Systems

A probabi l is t ic model is presented of a mul t ip rogrammed computer system operat ing under demand paging. The model contains an explicit represen ta t ion of sys tem overhead, the CPU requirements and paging character is t ics of the program load being described s ta t i s tically. Expressions for s teady-s ta te CPU problem program time, CPU overhead time, and channel ut i l izat ion are obtained. Some numerical results are given which quant i fy the gains in CPU uti l izat ion obta ined from mul t iprogramming. I t is also pointed out heur is t ica l ly and demonstrated numerical ly t h a t an actual decrease in CPU ut i l iza t ion results if there is too much overhead associated wi th mul t ip rogramming and if the average t ime be tween page exceptions decreases too rapidly wi th increasing number of mul t ip rogrammed jobs.

Collision-Free Access Control for Computer Communication Bus Networks

This paper considers access control for local area computer communication networks. We propose two distributed access control schemes for a bus network. The schemes are simple and asynchronous, and provide for collision-free communication among ports. In addition, one of the schemes provides a bounded, guaranteed time to transmisidon for each port. We also show that this scheme is efficient in the use of the bus bandwidth, in the sense that there is only a small fraction of time during which the bus is idle when there is at least one packet available for transmission.