Author: Michael Allen CranePublisher:
ISBN:
Category : Queuing theory
Languages : en
Pages : 118
Book Description
Limit Theorems for Queues in Transportation Systems
Author: Michael Allen CranePublisher:
ISBN:
Category : Queuing theory
Languages : en
Pages : 118
Book Description
Limit theorems for queues in transportation systems
Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 242
Book Description
Stochastic queueing models are formulated for three transportation systems. The first consists of a linear network of N+1 terminals served by S vehicles of fixed capacity. Customers arrive stochastically at terminal i, 1
Mathematical Methods in Queueing Theory
Author: A. B. ClarkePublisher: Springer Science & Business Media
ISBN: 3642808387
Category : Mathematics
Languages : en
Pages : 371
Book Description
On May 10-12, 1973 a Conference on Mathematical Methods in Graph Theory was held at Western Michigan University in Kalamazoo. The theme of this Conference was recent advances in the application of analytic and algebraic methods to the analysis of queues and queueing networks. In addition some discussion was given to statistical analy ses in queues, control problems and graphical methods. A total of 83 individuals from both industry and academic estab lishments participated in the Conference. A list of these partici pants can be found on page 373. A total of 18 papers were presented, with sUbstantial time being devoted to their informal discussion. This volume constitutes the proceedings of the Conference, and includes all papers presented. TABLE OF CONTENTS MARCEL F. NEUTS The Markov Renewal Branching Process • 1 RALPH L. DISNEY and W. PETER CHERRY Some Topics in Queueing Network Theory 23 JULIAN KEILSON Convexity and Complete Monotonicity in Queueing Distributions and Associated Limit Behavior . • • • • • . . • • • •• • • 45 G. F. NEWELL Graphical Representation of Queue Evolution for Multiple-Server Systems • . • • • • • • • • • • 63 N. U. PRABHU Wiener-Hopf Techniques in Queueing Theory 81 / IAJOS TAKACS Occupation Time Problems in the Theory of Queues 91 TAPAN P. BAGCHI and J. G. C. TEMPLETON Some Finite waiting Space Bulk Queueing Systems 133 U.
Weak Convergence Theorems for Queues in Heavy Traffic
Author: Ward WhittPublisher:
ISBN:
Category : Queuing theory
Languages : en
Pages : 436
Book Description
Limit theorems are proved for unstable queueing systems. The GI/G/1 queue is the primary concern, but the theorems apply to more general systems in which the various independence assumptions are relaxed. Bulk queues, queues with several servers (GI/M/s), queues with a finite waiting room, and dams are also discussed. (Author).
A Limit Theorem for Priority Queues in Heavy Traffic
Author: J. Michael HarrisonPublisher:
ISBN:
Category :
Languages : en
Pages : 21
Book Description
A single server, two priority queueing system is studied under the heavy traffic condition where the system traffic intensity is either at or near its critical value. An approximation is developed for the transient distribution of the low priority customers' virtual waiting time process. This result is stated formally as a limit theorem involving a sequence of systems whose traffic intensities approach the critical value. (Author).
Limit Theorems for Markov-modulated Queues
Author: Halldóra ThorsdottirPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
"This thesis considers queueing systems affected by a random environment. The behaviour of these queues is studied under specific asymptotic regimes. Embedding a queueing system in a random environment is a way to add flexibility to a model. This flexibility comes at the cost of increased complexity, in that the already stochastic arrival and service processes are also assumed to have randomly fluctuating parameters governed by the external environment. Here, scalings are applied to impose either a central limit theorem (CLT) type of scaling or a heavy traffic scaling. After speeding up the environment that modulates the Poisson arrivals to an infinite server queue, the arrival process is shown to be asymptotically Poisson with a uniform rate, see Chapter 2. By also speeding up the arrival rates, the scaled and centered queue length converges to a normally distributed random variable. The results are extended in Chapter 3 to a multi-dimensional CLT for an M/G/1 queue with Markov-modulation. Chapter 4 contains a functional CLT for the queue length with modulated arrivals using the martingale CLT to prove weak convergence to an OU process, where the environment moves either faster or slower than the arrival process. In Chapter 5, assuming a fairly general class of service disciplines, it is shown that the workload of an M/G/1 queue with modulated service capacity converges to an exponentially distributed random variable in heavy traffic. A special case of the queue is analysed under the discriminatory processor sharing discipline."--Samenvatting auteur.
Limit Theorems for Networks of Finite Buffer Queues in Heavy Traffic
Author: Sanjay MithalFunctional Limit Theorems for the Queue GI/G/1 in Light Traffic
Author: Stanford University. Department of Operations ResearchPublisher:
ISBN:
Category :
Languages : en
Pages : 28
Book Description
A GI/G/1 queueing system in light traffic has the property of returning to the idle state infinitely often. The purpose of the paper is to exploit this property to develop limit theorems for several processes generated by this system. The principal processes of interest are the following: W sub n, the waiting time of the nth customer; Q(t), the number of customers in the system at time t; W(t), the virtual waiting time at time t; B(t), the amount of time the server is busy in (O, t); I(t), the amount of tie the server is idle in (O, t); and D(t), the cumulative number of customers departing the system in (O, t).
Limit Theorems for Networks of Queues in Heavy Traffic
Author: Luiz Felipe MartinsMultiple Channel Queues in Heavy Traffic
Author: Donald L. IglehartPublisher:
ISBN:
Category : Queuing theory
Languages : en
Pages : 68
Book Description
Queueing systems with r arrival channels and s service channels are studied under the condition of heavy traffic: traffic intensity greater than or equal to one. Limit theorems are obtained for the random functions induced in D(0,1) by the following processes: total queue length, queue length at the ith server, total load, load at the ith server, virtual waiting time, waiting time of the nth arrival, number of departures, time of the nth arrival, and the time of the nth departure. Also limit theorems for certain functionals of the above processes are obtained as an immediate consequence of weak convergence.