Queuing Theory Model Research Articles

Optimal sharing of surgical costs in the presence of queues

We deal with a cost-allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context of several medical procedures, a certain demand for treatment and a maximum average waiting-time guaranteed by the government. We show that the sharing of an operating-theatre to treat patients of different medical disciplines leads to a cost reduction. We then compute an optimal fee per procedure for the use of the operating theatre, based on the Shapley value. Afterwards, considering the recovery time, we characterize the conditions under which the co-operation among treatments has a positive impact on the post-operative costs. Finally, a numerical example, constructed on the basis of real data, is provided to highlight the main features of our model.

Data Fusion Techniques for Adaptive Traffic Signal Control

Adaptive online traffic control in urban road networks requires information on the present and future traffic state. This information needs to be as complete and precise as possible. This paper introduces on the one hand a new method for online queue length determination based on data fusion technique (Mueck, 2002) and investigates on the other hand the performance gains that can be achieved employing this determination module as a quasi measurement with Kalman filtering technique in queuing theory models (e. g. Markovian chains). Both, the theoretical approach of the respective models as well as the results of simulation studies are presented.

Queuing theory models in urban passenger waterway transport terminals

This study aims at contributing to the development of future projects to design urban passenger waterway transport terminals, considering among other aspects, the boats used; the demand to be satisfied; and operational parameters such as the frequency or flow of boats, service intervals, and the passenger waiting time. The main critical points located in the terminal - bottlenecks - have been identified, where a large number of retained passengers can be found, contributing to the accumulation of queue. The vehicle arrival and service processes were analyzed with the use of Queuing Theory models. At the end of this research, some models of the Queuing Theory associated with methods for setting up traffic signal time were suggested as tools for optimizing time during loading and unloading of vehicles in the urban waterway transport terminals, in accordance with the model proposed by Brinati [l]. In order to validate the study, data were collected at the Silo Joaquim's urban waterway transport terminal, located in Salvador, Bahia - Brazil.

A Queueing Theory Model of Nonstationary Traffic Flow

The queueing-theoretical model for stationary traffic flow developed in a former paper is extended and modified for nonstationary flow. In particular it is shown how speed-flow-density relationships under nonstationary conditions may deviate from those obtained for stationary conditions. It is shown how the wide scatter which is often observed with empirical speed-flow-density data can be explained by nonstationarity. Furthermore, hysteresis loops, which may show up in speed-flow-density relationships, are interpreted by means of nonstationarity.

Stability of networks and protocols in the adversarial queueing model for packet routing

AbstractThe adversarial queueing theory model for packet routing was suggested by Borodin et al. We give a complete and simple characterization of all networks that are universally stable in this model. We show that the same characterization also holds for networks which are stable given that the packet forwarding protocol is FIFO (First in First out). We also show that a specific greedy protocol, SIS (Shortest in System), is stable against 0/1 stochastic adversaries. © 2001 John Wiley & Sons, Inc.

Effect of Seasonal Factors on Performance of Container Terminals

Within the last 20 years, the rapid growth of the container-handling industry has led Hong Kong to become one of the world's busiest container ports, with >11 million twenty-feet equivalent units (TEU) container throughput on a yearly basis. Furthermore, the yearly container throughput is expected to reach 15.5 million TEU by the year 2004. In this paper, an application of a queuing theory model to Hong Kong's Kwai Chung Container Terminals is developed and presented. More specifically, the effect of seasonal changes on the terminals is considered, paying particular attention to interarrival and service time of container vessels. Results show that including seasonal effects in the calculation can improve the accuracy of the model.

A queuing model analysis of the performance of the Hong Kong container terminals

The growth of container‐handling industry and its impact on Hong Kong's economy have aroused considerable attention in recent decades. Within the recent twenty years, the rapid growth of container‐handling industry has led Hong Kong to become one of the world's busiest container port with over 11 million T.E.U. s (Twenty Feet Equivalent Units) container throughput in one year period. Also the container throughput is expected to reach 15.5 million T.E.U. s by year 2004. As the success of container‐handling industry is significant, many studies have been conducted relating to this subject. In this paper, an application of a queuing theory model to Kwai Chung Container Terminals is developed and described. Specifically, we consider seasonal changes at the Terminals and focus on their effects on inter‐arrival time and service time of container vessel. A crucial component of the study relates to the empirical data collected. Besides verifying the validity of the model, those data provide guidelines for developing schemes to manage the seasonal fluctuation of container throughput of the Terminals.

Adaptive Packet Routing for Bursty Adversarial Traffic

One of the central tasks of networking is packet routing when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separation has a serious drawback: each packet's path is fixed at the source and cannot be modified adaptively en-route. The problem is especially severe when packet injections are modeled by an adversary, whose goal is to cause traffic-jams. In this paper, we consider this adversarial setting, motivated by the adversarial queuing theory model of Borodin et al. (1996, in “Proc. of 28th STOC,” pp. 376–385). More precisely, we consider an adversary who injects packets, with only their destinations specified, into network nodes in a continuous manner subject to certain limitations on the injection rate. The question whether it is possible to deal with such an adversary and to design protocols that would discover routes which avoid traffic jams so that nodes only store a bounded number of packets was left as an open problem by Andrews et al. (1997, in “Proc. of 38th FOCS,” pp. 294–302) (who deal with the nonadaptive case where the adversary provides routes for the packets). In the present paper, we resolve this open problem. In particular, we present a simple, deterministic, local-control protocol that applies to any network topology. Our protocol guarantees that, for any injection sequence generated by the adversary, the buffers at the nodes are polynomially bounded and that each packet has a polynomially bounded delivery time.

Real-time queueing theory: A tutorial presentation with an admission control application

Real-time scheduling, or scheduling with respect to a deadline, is critical in many application areas such as telecommunications, control systems, and manufacturing. This paper presents a novel approach to real-time scheduling based on a queueing theory model. Using real-time queueing theory (RTQT), one can analytically determine the distribution of the lead-time profile (i.e., the time until the deadline is reached) of customers waiting for service. Emphasis is placed on the development of the equations used to determine the lead-time profile distribution. The development of the GI/G/1 case is presented and confirmed using simulation. Simulation results confirm prior research for the M/M/1 and GI/M/1 case. As a practical application, RTQT is used to implement a packet admission control algorithm for a telecommunications network. Using this algorithm, packet lateness was reduced by up to 31%.

A Queuing Theory Model for Book Reservations and Circulation

Queuing theory has long been a popular choice, as a quantitative framework for describing book circulation models. The model developed in this article uses simple queuing theory to help describe the book circulation and reservation process. The queue is formed by customers making reservations for the book when it is not available in the library, and their propensity to make a reservation is governed by the expected waiting time before receiving the book.

Queueing at unsignalized intersections

A general queueing theory model for traffic flow at unsignalized intersections is described and analysed which contains most of the mathematical models developed in the literature as special cases. Thus a consistent approach is presented for obtaining these models from a general viewpoint. Included are green-red models which are based on an analogy to traffic signals. Critical gaps and merging times or move-up times are allowed to be stochastically dependent. Inconsistent and consistent driver behaviour is considered. Platooning of the major road traffic with random intra-bunch headways is included. The results focus on the distributions of queue lengths and delays and, in particular, on capacities. A general capacity formula is developed and it is shown how the various capacity formulas from the literature come out as special cases. Some numerical results are presented.

The Queueing Maximal availability location problem: A model for the siting of emergency vehicles

The Maximal Availability Location Problem (MALP) has been recently formulated as a probabilistic version of the maximal covering location problem. The added feature in MALP is that randomness into the availability of servers is considered. In MALP, though, it is assumed that the probabilities of different servers being busy are independent. In this paper, we utilize results from queuing theory to relax this assumption, obtaining a more realistic model for emergency systems: the Queueing MALP or Q-MALP. We also consider in this model that travel times or distances along arcs of the network are random variables. We show here how to site limited numbers of emergency vehicles, such as ambulances, in such a way as to maximize the calls for service which have an ambulance available within a time or distance standard with reliability α — using a queueing theory model for server availability. We also propose some extensions to the basic model. Formulations are presented and computational experience is offered.

Introduction to computer performance analysis with Mathematica

Capacity Planning. Understanding the Current Environment. Setting Performance Objectives. Prediction of Future Workload. Evaluation of Future Configurations. Validation. The Ongoing Management Process. Performance Management Tools. Organizations and Journals for Performance Analysis. Components of Computer Performance: Central Processing Units. The Memory Hierarchy. Input Output. Basic Calculations: Model Definitions, Single Workload Class Models. Multiple Workloads Models. Basic Queueing Network Theory. Queue discipline. Queueing Network Performance. Queueing Network Laws. Little's Law. Utilization Law . Response Time Law. Forced Flow Law. Bounds and Bottlenecks. Bounds for Single Class Networks. Modeling Study Paradigm. Advantages of Queueing Theory Models. Analytic Solution Methods: Analytic Queueing Theory Network Models. Single Class Models. Multiclass Models. Priority Queueing Systems. Modeling Main Computer Memory. Model Parameterization: Measurement Tools. Model Parameterization. The Modeling Paradigm. Calculating the Parameters. Simulation and Benchmarking: Introduction to Simulation. Writing a Simulator. Simulation Languages. Simulation Summary. Benchmarking. Forecasting: NFU Time Series Forecasting. Afterward.

Optimising the number of load-haul-dump machines in a Swedish mine by using queuing theory: A case study

ABSTRACT This paper discusses the determination of optimal number of Load-Haul-Dump (LHD) machines for a given mine using queuing theory model. The number of LHDs is determined by taking into account the performance of LHD, the performance of repairshop, and economic factors such as operators salary, maintenance cost, price of an LHD machine, etc. It is shown with example that queuing model can accurately calculate the probability of a given number of LHD machines for production. This paper also illustrates with an example that the number of LHD machines estimated by using queuing model is more accurate compare to the method using binomial distribution, etc. The example used in this paper is from a Swedish mine.

Modeling of the DZero data acquisition system

A queuing theory model was used in the initial design of the DZero data acquisition system. It was mainly used for the front-end electronic systems. Since then the model has been extended to include the entire data path for the tracking system. The tracking system generates the most data, and this system will determine the overall transfer rate. The model was developed using both analytical and simulation methods for solving a series of single-server queues. The model and the methods used to develop it are described. Results from the original methods, updated calculations representing the system as built, and comparisons with measurements made with the hardware in place for the cosmic ray test run are presented. >

Aperiodic task scheduling for Hard-Real-Time systems

This thesis develops the Sporadic Server (SS) algorithm for scheduling aperiodic tasks in real-time systems. The SS algorithm is an extension of the rate monotonic algorithm which was designed to schedule periodic tasks. This thesis demonstrates that the SS algorithm is able to guarantee deadlines for hard-deadline aperiodic tasks and provide good responsiveness for soft-deadline aperiodic tasks while avoiding the schedulability penalty and implementation complexity of previous aperiodic service algorithms. It is also proven that the aperiodic servers created by the SS algorithm can be treated as equivalently-sized periodic tasks when assessing schedulability. This allows all the scheduling theories developed for the rate monotonic algorithm to be used to schedule aperiodic tasks. For scheduling aperiodic and periodic tasks that share data, this thesis defines the interactions and schedulability impact of using the SS algorithm with the priority inheritance protocols. For scheduling hard-deadline tasks with short deadlines, an extension of the rate monotonic algorithm and analysis is developed. To predict performance of the SS algorithm, this thesis develops models and equations that allow the use of standard queueing theory models to predict the average response time of soft-deadline aperiodic tasks serviced with a high-priority sporadic server. Implementation methods are also developed to support the SS algorithm in Ada and on the Futurebus+.

Signalized intersections with variable flow rates: II A model for delay estimation

AbstractThis second part of our work develops a model for delay estimation at intersections whose traffic signal controls are continuously being updated. Generally, these traffic signals are centrally controlled. The foundation for the delay estimation model is based on a queuing theory model called “Preemptive resume discipline for M/G/1 with two priority levels.” This queuing model assumes that two customers arrive at acertain point by a Poisson arrival process, and that one customer has service priority over the second customer. The analogy for the case of intersection control is that the preferred customers are the red lights and the secondary customers are the vehicles. In order to adapt the model to the realistic behavior of vehicle traffic at continuously adjusted signals, components are derived to modify the model. The simulation results of the first part of this work are used to calculate adjustment factors that fairly accurately reproduce the simulated delays. This gives rise to the advantage of using in practice a closed mathematical model, in particular when trying to optimize the operation of signalized intersections at the network level.

The application of queueing models to strategies for reducing prison population size

This article examines the use of well known queueing theory models to investigate the effectiveness of strategies for reducing prison population size. These strategies are (1) reduced or zero inmate admissions, (2) immediate release of some inmates, and (3) a reduction of the average time incarcerated. The usefulness of the quantitative models presented lies in their being able todetermine for any one of the strategies the likelihood of obtaining a prescribed reduction in prison population size within a preselected time interval. Parameter values can be changed in the model, allowing examination of a wide range of possibilities.

A model for obtaining waiting time estimates in an interactive computing environment

A queueing theory model is described which serves as a management tool for evaluating the service efficiency of a computer installation. Analysis relies on standard data obtained at low cost. Application results are shown for the case of a Prime 750 system which supports an heterogeneous population of interactive users.

Statistical analysis of the usage of a computer system

This paper is concerned with an empirical investigation of a common and important type of computer system and usage in business applications, viz., querying, updating and modifying a large database. Specifically, it describes the analysis of data collected from such an application and addresses two issues. Firstly, it assesses the applicability of statistical assumptions that underlie certain widely-used queueing theory models for computer systems usage. Secondly, it investigates measures of usage, as well as relationships among them, that may serve as appropriate bases for a pricing scheme for usage of computer systems of the type considered here.