Stochastic inequalities between customer-stationary and time-stationary characteristics of queueing systems with point processes

1980 ◽  
Vol 17 (3) ◽  
pp. 768-777 ◽  
Author(s):  
D. König ◽  
V. Schmidt
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Queueing Systems ◽  
Marked Point Processes ◽  
Stationary Processes ◽  
Conservation Principle ◽  
Intensity Conservation Principle

By means of a general intensity conservation principle for stationary processes with imbedded marked point processes (PMP) stochastic inequalities are proved between customer-stationary and time-stationary characteristics of queueing systems G/G/s/r.

Stochastic inequalities between customer-stationary and time-stationary characteristics of queueing systems with point processes

1980 ◽  
Vol 17 (03) ◽  
pp. 768-777 ◽  
Author(s):  
D. König ◽  
V. Schmidt
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Queueing Systems ◽  
Marked Point Processes ◽  
Stationary Processes ◽  
Conservation Principle ◽  
Intensity Conservation Principle

By means of a general intensity conservation principle for stationary processes with imbedded marked point processes (PMP) stochastic inequalities are proved between customer-stationary and time-stationary characteristics of queueing systemsG/G/s/r.

Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes

1980 ◽  
Vol 17 (3) ◽  
pp. 753-767 ◽  
Author(s):  
D. König ◽  
V. Schmidt
Keyword(s):  
Queueing Theory ◽  
Point Processes ◽  
Marked Point ◽  
Queueing Systems ◽  
Service Systems ◽  
Marked Point Processes ◽  
Service Rate ◽  
Unified Approach ◽  
Intensity Conservation Principle ◽  
Continuous Time Processes

In this paper a unified approach is used for proving relationships between customer-stationary and time-stationary characteristics of service systems with varying service rate and point processes. This approach is based on an intensity conservation principle for general stationary continuous-time processes with imbedded stationary marked point processes. It enables us to work under weaker independence assumptions than usual in queueing theory.

Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes

1980 ◽  
Vol 17 (03) ◽  
pp. 753-767 ◽  
Author(s):  
D. König ◽  
V. Schmidt
Keyword(s):  
Queueing Theory ◽  
Point Processes ◽  
Marked Point ◽  
Queueing Systems ◽  
Service Systems ◽  
Marked Point Processes ◽  
Service Rate ◽  
Unified Approach ◽  
Intensity Conservation Principle ◽  
Continuous Time Processes

In this paper a unified approach is used for proving relationships between customer-stationary and time-stationary characteristics of service systems with varying service rate and point processes. This approach is based on an intensity conservation principle for general stationary continuous-time processes with imbedded stationary marked point processes. It enables us to work under weaker independence assumptions than usual in queueing theory.

scholarly journals Palm theory for random time changes

2001 ◽  
Vol 14 (1) ◽  
pp. 55-74 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Gert Nieuwenhuis ◽  
Karl Sigman
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Queueing Systems ◽  
Random Time ◽  
Marked Point Processes ◽  
Random Measures ◽  
Important Special Case ◽  
Dimensional Group ◽  
Starting Point ◽  
Time Changes

Palm distributions are basic tools when studying stationarity in the context of point processes, queueing systems, fluid queues or random measures. The framework varies with the random phenomenon of interest, but usually a one-dimensional group of measure-preserving shifts is the starting point. In the present paper, by alternatively using a framework involving random time changes (RTCs) and a two-dimensional family of shifts, we are able to characterize all of the above systems in a single framework. Moreover, this leads to what we call the detailed Palm distribution (DPD) which is stationary with respect to a certain group of shifts. The DPD has a very natural interpretation as the distribution seen at a randomly chosen position on the extended graph of the RTC, and satisfies a general duality criterion: the DPD of the DPD gives the underlying probability P in return.To illustrate the generality of our approach, we show that classical Palm theory for random measures is included in our RTC framework. We also consider the important special case of marked point processes with batches. We illustrate how our approach naturally allows one to distinguish between the marks within a batch while retaining nice stationarity properties.

Marked point processes as limits of Markovian arrival streams

1993 ◽  
Vol 30 (02) ◽  
pp. 365-372 ◽  
Author(s):  
Søren Asmussen ◽  
Ger Koole
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
The State ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
State Transitions ◽  
Poisson Arrival ◽  
Convergence Of Moments ◽  
Environmental Process

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

Some EATA properties for marked point processes

1995 ◽  
Vol 32 (04) ◽  
pp. 922-929
Author(s):  
D. Kofman ◽  
H. Korezlioglu
Keyword(s):  
Point Processes ◽  
Stochastic Integral ◽  
Marked Point ◽  
Marked Point Processes ◽  
Batch Arrival ◽  
Integral Approach ◽  
Arrival Processes

We derive an ESTA property for marked point processes similar to Wolff's PASTA property for ordinary (non-marked) point processes, via a stochastic integral approach. This new ESTA property allows us to extend a known result on the conditional PASTA property and to derive an ASTA property for batch arrival processes. We also present an application of our results.

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