Dual processes to solve single server systems

SummaryIn a previous paper [4] the author studied the stochastic process {wn, n = 1,2, …}, recursively defined by with K a positive constant, τ1, τ2, … σ1, σ2, …, independent, nonnegative stochastic variables. τ1,τ2…, are identically distributed, and σ1,σ2,…, are also identically distributed variables. For this process the generating function of the Laplace-Stieltjes transforms of the joint distribution of Wn, σ2 + … + σn and τ1 + … + τn−1 has been obtained. Closely related to the process {wn, n = 1, 2,…} is the process {un, n = 1, 2,…} with {un = K + [wn + τn − K]−, n = 1,2,…; these are dual processes.In the present paper we study the stationary distributions of the processes {wn, n= 1,2, …} and {un, n = 1,2, …}, and the distributions ot the entrance times and return times of the events “wn, n = 0” and “un = K” for some n, for discrete as well as for continuous time. For these events various taboo probabilities are also investigated. The mathematical descri ption of the processes {wn, n = 1,2, …} and {un, n= 1,2, …} gives all the necessary information about the time-dependent behaviour for the general dam model with finite capacity K, since the process {wn, n= 1,2, …} is the basic process for such dam models. In Sections 5, 6 and 7 the general theory is applied to the models M/G/1 and G/M/1. Complete explicit solutions are obtained for these models.The present theory also leads to new and important results for the queueing system or dam model G/G/1 with infinite capacity. For instance the joint distribution of the busy period (or wet period) and of the supremum of the dam content dunng this period is obtained.

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LOCKING PROTOCOL FOR INFORMATION FLOW CONTROL

Journal of Interconnection Networks ◽

10.1142/s0219265904001143 ◽

2004 ◽

Vol 05 (03) ◽

pp. 233-247 ◽

Cited By ~ 2

Author(s):

RYUNG CHON ◽

KOUHEI TAKEDA ◽

TOMOYA ENOKIDO ◽

MAKOTO TAKIZAWA

Keyword(s):

Access Control ◽

Flow Control ◽

Information Flow ◽

Single Server ◽

Role Based Access Control ◽

Information Flow Control ◽

Server Systems ◽

Locking Protocol ◽

Role Based ◽

Multi Server

We discuss a novel role locking protocol (RLP) to prevent illegal information flow among objects in a role-based access control (RBAC) model. In this paper, we define a conflicting relation among roles "a role R1 conflicts with another role R2" to show that illegal information flow may occur if a transaction associated with role R1 is performed before another transaction with role R2. Here, we introduce a role lock on an object to abort a transaction with role R1 if another transaction with role R2 had been already performed on the object. Role locks are not released even if transactions issuing the role locks commit. After data in an object o1 flow to another object o2, if the object o1 is updated, the data in the object o2 is independent of the object o1, i.e. obsolete. A role lock on an object can be released if information brought into the object is obsolete. We discuss how to release obsolete role locks. We also discuss how to implement the role locking protocol in single-server and multi-server systems.

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Optimal scheduling in some multi-queue single-server systems

Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration ◽

10.1109/infcom.1990.91376 ◽

2002 ◽

Cited By ~ 1

Author(s):

Z. Liu ◽

P. Nain

Keyword(s):

Optimal Scheduling ◽

Single Server ◽

Server Systems

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Exponential spectra as a tool for the study of server-systems with several classes of customers

Journal of Applied Probability ◽

10.1017/s0021900200105686 ◽

1978 ◽

Vol 15 (01) ◽

pp. 162-170 ◽

Cited By ~ 3

Author(s):

J. Keilson

Keyword(s):

Waiting Time ◽

Busy Period ◽

Heavy Traffic ◽

Transient Behavior ◽

Single Server ◽

Idle State ◽

Priority Systems ◽

Completely Monotone ◽

Server Systems ◽

Server System

For a single-server system having several Poisson streams of customers with exponentially distributed service times, busy period densities, waiting time densities, and idle state probabilities are completely monotone. The exponential spectra for such densities are of importance for understanding the transient behavior of such systems. Algorithms are given for the computation of such spectra. Applications to heavy traffic situations and priority systems are also discussed.

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On two stationary distributions for the stable GI/G/1 queue

Journal of Applied Probability ◽

10.1017/s0021900200118303 ◽

1974 ◽

Vol 11 (04) ◽

pp. 849-852 ◽

Cited By ~ 4

Author(s):

Austin J. Lemoine

Keyword(s):

Waiting Time ◽

Queue Length ◽

Distribution Functions ◽

Single Server ◽

Stationary Distributions ◽

Virtual Waiting Time ◽

Server Systems ◽

Stationary Queue Length

This paper provides simple proofs of two standard results for the stable GI/G/1 queue on the structure of the distribution functions of the stationary virtual waiting time and the stationary queue-length Our argument is applicable to more general single server systems than the queue GI/G/1.

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