Michael A. Zazanis

Push and pull production systems: issues and comparisons

Concerns about American manufacturing competitiveness compel new interest in alternative production control strategies. In this paper, we examine the behavior of push and pull production systems in an attempt to explain the apparent superior performance of pull systems. We consider three conjectures: that pull systems have less congestion; that pull systems are inherently easier to control; and that the benefits of a pull environment owe more to the fact that WIP is bounded than to the practice of “pulling” everywhere. We examine these conjectures for analytically tractable models. In doing so, we not only find supporting evidence for our surmises but also identify a control strategy that has push and pull characteristics and appears to outperform both pure push and pure pull systems. This hybrid system also appears to be more general in its applicability than traditional pull systems such as Kanban.

Conservation laws and reflection mappings with an application to multiclass mean value analysis for stochastic fluid queues

In this paper we derive an alternative representation for the reflection of a continuous, bounded variation process. Under stationarity assumptions we prove a continuous counterpart of Littles law of classical queueing theory. These results, together with formulas from Palm calculus, are used to explain the method for the derivation of the mean value of a buffer fed by a special type stochastic fluid arrival process.

Convergence rates of finite-difference sensitivity estimates for stochastic systems

A mean square error analysis of finite-difference sensitivity estimators for stochastic systems is presented and an expression for the optimal size of the increment is derived. The asymptotic behavior of the optimal increments, and the behavior of the corresponding optimal finite-difference (FD) estimators are investigated for finite-horizon experiments. Steady-state estimation is also considered for regenerative systems and in this context a convergence analysis of ratio estimators is presented. The use of variance reduction techniques for these FD estimates, such as common random numbers in simulation experiments, is not considered here. In the case here, direct gradient estimation techniques (such as perturbation analysis and likelihood ratio methods) whenever applicable, are shown to converge asymptotically faster than the optimal FD estimators.

Sensitivity analysis for stationary and ergodic queues

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits

Perturbation analysis of the GI/GI/1 queue

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,θ), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect toθ. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.

Sample path analysis of level crossings for the workload process

We examine level crossings of sample paths of queueing processes and investigate the conditions under which the limiting empirical distribution for the workload process exists and is absolutely continuous. The connection between the density of the workload distribution and the rate of downcrossings is established as a sample path result that does not depend on any stochastic assumptions. As a corollary, we obtain the sample path version of the Takács formula connecting the time and customer stationary distributions in a queue. Defective limiting empirical distributions are considered and an expression for the mass at infinity is derived.

Sensitivity analysis for stationary and ergodic queues: additional results

Perturbation analysis estimators for expectations of possibly discontinuous functions of the time-stationary workload were derived in [2]. The expressions obtained may, however, not be valid if the customer-stationary distribution of the workload has atoms (at points other than zero). This was pointed out by Br6maud and Lasgouttes in [1]. In this note we clearly state the additional condition required for the validity of the expressions in [2]. We furthermore show how our approximation scheme can also be used to obtain the correct expressions for the right and left derivatives given in [1]. STATIONARY PROCESSES; PERFORMANCE EVALUATION AND QUEUEING; NONMARKOVIAN PROCESSES ESTIMATION AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60K25 SECONDARY 34D10

A sample path analysis of M/GI/1 queues with workload restrictions

A simple random time change is used to analyze M/GI/1 queues with workload restrictions. The types of restrictions considered include workload bounds and rejection of jobs whose waiting times exceed a (possibly random) threshold. Load dependent service rates and vacations are also allowed and in each case the steady state distribution of the workload process for the system with workload restrictions is obtained in terms of that of the corresponding M/ GI/1 queue without restrictions. The novel sample path arguments used simplify and generalize previous results.

Consistency of perturbation analysis for a queue with finite buffer space and loss policy

The subject of discrete-event dynamical systems has taken on a new direction with the advent of perturbation analysis (PA), an efficient method for estimating the gradients of a steady-state performance measure, by analyzing data obtained from a single-simulation experiment in the time domain. A crucial issue is whether PA gives strongly consistent estimates, namely, whether average time-domain-based gradients converge, over infinite horizon, to the steady-state gradients. In this paper, we investigate this issue for a queue with a finite buffer capacity and a loss policy. The performance measure in question is the average amount of lost customers, as a function of the buffers capacity, which is assumed to be continuous in our work. It is shown that PA gives strongly consistent estimates. The analysis uses a new technique, based on busy period-dependent inequalities. This technique may have possible extensions to analyses of consistency of PA for more general queueing systems.

Synchronized queues with deterministic arrivals

We consider m independent exponential servers in parallel, driven by the same deterministic input. This is a modification of the Flatto-Hahn-Wright model which turns out to be easily tractable. We focus on the time-stationary distribution of the number of customers which is obtained using the Palm inversion formula.