Simple Queueing Research Articles

On the influence of resequencing on the regularity of service

The purpose of this paper is to study how resequencing packets in a communication network may affect the performance of the application needing the information. We analyze a simple queueing model where customers may be randomly disordered, before arriving at a single server queue. The performance index chosen is the variance of the server waiting time, which is a measure of the `jitter' suffered by the application. The analysis reveals that not resequencing customers does improve the service regularity for a wide range of loss probabilities and service times. It shows also that, contrary to the conclusions of previous analyses, resequencing does not necessarily make the performance of the system worse.

Performance and Efficiency in DistributedEnterprise Management

This paper is motivated by the increasing need for scaleable, distributed management architectures for integrated network, system and application management within the enterprise network environment. Such integration, extension and wide area deployment of management functionality impose heavy performance requirements and produce increased management traffic. Aiming to minimize this traffic and the overall response time, we propose a distributed hierarchical caching scheme that attempts to take advantage of the diverse consistency requirements of management applications. We define coherency conditions and update policies, identify the appropriate interaction semantics, and discuss an SNMP-based implementation. In order to evaluate the proposed model and to quantify the expected performance gains we construct a simple queuing model that provides analytical results on the improvement of response time and the reduction of management traffic. Finally, the analysis of experimental results provides some insight on performance improvement for specific classes of managed objects.

Stochastic comparison results for non-blocking switches with output queueing

We propose a systematic approach to quantify the impact of nonuniform traffic on the performance of non-blocking switches with output queueing. We do so in the context of a simple queueing model where cells arrive to input ports according to independent Bernoulli processes, and are switched to an output port under a random routing mechanism. We give conditions on pairs of input rate vectors and switching matrices which ensure various stochastic comparisons for performance measures of interest. These conditions are formulated in terms of the majorization ordering while the comparison results are expressed in the strong and convex increasing orderings

Traffic sampling methods for end-to-end QoS evaluation in large heterogeneous networks

Research, education and business infrastructures based on large heterogeneous networks pose a new class of management problems such as on-line end-to-end performance monitoring over packet switched networks in support of multimedia services. A test and measurement system able to monitor the status of packet networks at end-to-end level and to evaluate the quality of service actually provided to the end users is presented in this paper. The basic idea behind the proposed solution is the introduction of sampling techniques in the measurement and estimation phases, in order to reduce the quantity of control data, of resources required to process it and hence to speed up all the further management functions. Sampling is introduced for relieving the complexity of these functions, which are usually carried out by means of heavy routines dealing with huge amount of data. The analysis is carried out by means of simulation on a very simple queueing model loaded by synthetic traffic and actual traces collected over an intercontinental ATM trunk. The rationale behind this choice is the search for a trade-off between the sampling rate and attained estimation accuracy, representing a theoretical and quantitative method usable by network operators to design new control tools.

Queueing for Toilets

The New Zealand Works Consultancy Services was contracted to study of the number of sanitary facilities to be provided in buildings, in order to revise the tables in the New Zealand Building Code. A very extensive data-gathering exercise to predict occupancy times and demand for various kinds of buildings was carried out. Simple queueing models proved to be the most appropriate tools Jor use to estimate the waiting times that the new standards would produce. While the aim of the project was to produce consistent standards, a preliminary analysis indicated the new standards might produce savings with a NPV of about $80 million.

Neurocontroller for buffer overload control in a packet switch

The authors describe a buffer overload control scheme, which adaptively matches the buffer input rate to prevailing conditions in the queueing system, for efficient utilisation of the system resources. They propose an adaptive feedback control algorithm which uses neural network modelling of the system dynamics and a gradient-based control optimisation technique for buffer overload control. Using a simple dynamic queueing model, it is shown that this technique can regulate buffer occupancy levels (or queueing delays) to minimise congestion in the queueing system.

Propagation of Chaos for Queueing Networks

We consider propagation of chaos phenomena for closed Markovian queueing networks with increasing numbers of nodes. The queues at different nodes behave themselves asymptotically as independent simple queues. Convergence rate estimates are obtained for the maximum similarity case.

Extreme value theory for queues via cycle maxima

The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum $overline X( au)$ of the queueing process ${X(t)}$ during a regenerative cycle $ au$. For simple queues, methods for obtaining the distribution of $overline X( au)$ both explicitly and asymptotically are reviewed. In greater generality, the study leads to Wiener-Hopf problems. Extensions to queues in a Markov regime, for example, to those governed by Markov-modulated Poisson arrivals, are also considered.

Long range dependence of point processes, with queueing examples

Possible definitions of the long range dependence (LRD) of a stationary point process are discussed. Examples from the standard queueing literature are considered and shown to be amenable to yielding processes with long range count dependence. In particular the effect of the single-server queueing operator, whereby one point process is transformed into another via the mechanism of a simple queue, is examined for possible long range dependence of both the counting and interval properties of the output process. For an infinite server queue, the output is long range count dependent if and only if the input is long range count dependent.

A simulation clock-based solution to the frequency domain experiment indexing problem

Frequency domain experiments (FDEs) were introduced to perform system sensitivity analysis for factor screening in complex simulations. Since then, FDEs have been used in simulation optimization, gradient estimation and several other research areas. Central to all FDEs is the Fourier analysis of a sampled data sequence. The choice of an appropriate oscillation index and associated sampling index for the sampled data sequence has been a much researched topic now known in the FDE literature as the indexing problem. In this paper we address the indexing problem by providing some general guidelines on the selection of the oscillation index and considering the implementation of two different indices: the continuous global simulation clock time and an inherently discrete index such as the job index in a simple queuing system. We show that the choice of a discrete oscillation index has to be made in an application-dependent manner and does not generalize well to different discrete-event simulation scenarios. In contrast, because the notion of time underlies all discrete-event simulations, the global simulation clock time is a natural choice for an FDE indexing scheme. Two different schemes for the global simulation clock time are presented. The results are illustrated via different scenarios commonly found in simulations of queuing networks and manufacturing systems.

Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales

This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. For the case of Poisson demands and exponential production times, we show that the optimal policy can be characterized by a sequence of monotone stock rationing levels. For each demand class, there exists a stock rationing level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher priority demands. A simple queueing model is analyzed to compute the operating cost of a rationing policy. In a numerical study, we compare the optimal rationing policy with a first-come first-served policy to investigate the benefit of stock rationing under different operating conditions of the system.

Travel Time Prediction in Urban Road Networks

Abstract The prediction of travel times in road networks is a basic component of many traffic monitoring and control systems. This paper extends the simple queueing model described in Kimber and Daly (1986) to use the value of the detector occupancy per cycle, in addition to the vehicle count, in order to predict link travel times from readily-available detector inputs. The model was fitted to simulated data from the VISSIM microscopic traffic simulation tool and performed well in validation on an independently generated data-set. Tests with SCOOT data gathered by the Instrumented City facility were also encouraging.

RPA: a simple, efficient, and flexible policy for input buffered ATM switches

Reservation with Preemption and Acknowledgment (RPA) is a simple, efficient, and flexible queuing discipline and scheduling algorithm for input buffered asynchronous transfer-mode (ATM) switches. This letter describes the RPA algorithms, and presents simulation results to demonstrate the effectiveness of the proposed approach.

Interval Coverage in Multiclass Queues Using Batch Mean Estimates

We investigate the fixed, sample-size, batch-mean procedure for creating confidence intervals from simulated data obtained from a stochastic queueing system with multiple customer classes. We show that, for a multiclass M/M/1 queue, serial correlation between customers of the same class decreases to zero as the number of customer classes increases. We also derive a closed-form expression for the asymptotic variance of waiting time by customer type. We then empirically examine batch-mean estimator coverage for a simple queue with multiple customer classes. We find that batch-mean estimators perform better in terms of coverage and interval half width in multiclass queues, with a fixed number of observations per class, than in the traditionally studied single-class systems. We also examine the effect of multiple classes where the total computational effort remains fixed.

An Introduction to Queueing Theory

Generating functions simple queues birth-death models the M/G/1 system the embedded Markov process other models for single-server queues random arrivals, block service, constant interval between times at which service is available transient solutions networks of queues simulation models appendix.

Queueing models and stability of message flows in distributed simulators of open queueing networks

In this paper we study message flow processes in distributed simulators of open queueing networks. We develop and study queueing models for distributed simulators with maximum lookahead sequencing. We characterize the "external'' arrival process, and the message feedback process in the simulator of a simple queueing network with feedback. We show that a certain "natural'' modelling construct for the arrival process is exactly correct, whereas an ``obvious'' model for the feedback process is wrong; we then show how to develop the correct model. Our analysis throws light on the stability of distributed simulators of queueing networks with feedback. We show how the stability of such simulators depends on the parameters of the queueing network.

Execution time analysis of communicating tasks in distributed systems

Task-execution times are one of the most important parameters in scheduling tasks. Most scheduling algorithms are based on the assumption that either worst-case task-execution times are known to the scheduler or no information on execution times is available at all. While scheduling tasks based on worst-case execution times can guarantee to meet their timing requirements, it may lead to severe under-utilization of CPUs because worst-case execution times could be one or two orders of magnitude larger than the corresponding actual values. Scheduling tasks based on the execution time distribution (instead of worst-case execution times) is known to improve system utilization significantly. In this paper, we propose a model to predict task execution times in a distributed system. The model considers several factors which affect the execution time of each task. These factors are classified into two groups: intrinsic and extrinsic. The intrinsic factors control the flow within a task, while the extrinsic factors include communication and synchronization delays between tasks. By simplifying the extrinsic factors, we represent a distributed system with a simple queuing model. The proposed queuing model consists of two stations: one for computation and the other for communication and synchronization.

A Scaled Stochastic Approximation Algorithm

Consider a stochastic system of such complexity that its performance can only be evaluated by using simulation or direct experimentation. To optimize the expected performance of such systems as a function of several continuous input parameters (decision variables), we present a “scaled” stochastic approximation algorithm for finding the zero (root) of the gradient of the response function. In each iteration of the scaled algorithm, two independent gradient estimates are sampled at the current estimate of the optimal input-parameter vector to compute a scale-free estimate of the next search direction. We establish sufficient conditions to ensure strong consistency and asymptotic normality of the resulting estimator of the optimal input-parameter vector. Strong consistency is also established for a variant of the scaled algorithm with Kesten's acceleration. An experimental performance comparison of the scaled algorithm and the classical Robbins-Monro algorithm in two simple queueing systems reveals some of the practical advantages of the scaled algorithm.

An experimental analysis of steady state convergence in simple queueing systems: Implications for flexible manufacturing system models

Queueing models are widely used for performance analysis of Flexible Manufacturing Systems (FMS). Most studies are done under steady state assumptions. The inherent flexibility of FMS in terms of input, volume, and mix makes such an assumption hard to justify. In this paper, we investigate the convergence rate to steady state in simple queueing models that constitute the basic building blocks of more complex FMS models. The study reveals that steady-state conditions are not achieved during the execution of batches of moderate size. We therefore conclude that although equilibrium models are appropriate for studying long-term planning problems, for the operational control of FMSs, it is highly desirable to study the transient behaviour of the system. On a broader scope, our investigation also shows that steady-state assumptions used in the analysis of any inherently transient system should be carefully validated.

Exploiting Partial Information in Queueing Systems

We often try to draw inferences from partial observations of queueing systems in real-life situations. For example, if we observe many customer arrivals, we may presume that the system is crowded and many customers are served. Unfortunately, such an intuitive statement is not necessarily valid. We provide sufficient conditions under which the intuition can be justified, and investigate related properties of queueing systems. We also study a way to exploit the partial information in a quantitative manner for simple queueing systems. One numerical result is rather counterintuitive. Specifically, the number of customers in the system at time t given that the cumulative number of departures is a certain constant is not necessarily stochastically increasing in t for a simple M/M/1 system with finite capacity.