Simple derivations of the invariance relations and their applications

1982 ◽  
Vol 19 (1) ◽  
pp. 183-194 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
General Formula ◽  
Waiting Time ◽  
Simple Proof ◽  
Inversion Formula ◽  
Point Processes ◽  
Queueing Models ◽  
Unified Approach ◽  
Little's Formula

In the literature, various methods have been studied for obtaining invariance relations, for example, L = λW (Little's formula), in queueing models. Recently, it has become known that the theory of point processes provides a unified approach to them (cf. Franken (1976), König et al. (1978), Miyazawa (1979)). This paper is also based on that theory, and we derive a general formula from the inversion formula of point processes. It is shown that this leads to a simple proof for invariance relations in G/G/c queues. Using these results, we discuss a condition for the distribution of the waiting time vector of a G/G/c queue to be identical with that of an M/G/c queue.

Simple derivations of the invariance relations and their applications

1982 ◽  
Vol 19 (01) ◽  
pp. 183-194 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
General Formula ◽  
Waiting Time ◽  
Simple Proof ◽  
Inversion Formula ◽  
Point Processes ◽  
Queueing Models ◽  
Unified Approach ◽  
Little's Formula

In the literature, various methods have been studied for obtaining invariance relations, for example, L = λW (Little's formula), in queueing models. Recently, it has become known that the theory of point processes provides a unified approach to them (cf. Franken (1976), König et al. (1978), Miyazawa (1979)). This paper is also based on that theory, and we derive a general formula from the inversion formula of point processes. It is shown that this leads to a simple proof for invariance relations in G/G/c queues. Using these results, we discuss a condition for the distribution of the waiting time vector of a G/G/c queue to be identical with that of an M/G/c queue.

Relations Among Moments of Waiting Time and Queue Size Distribution in Bulk Queueing Systems

1987 ◽  
Vol 36 (1-2) ◽  
pp. 63-68
Author(s):  
A. Ghosal ◽  
S. Madan ◽  
M.L. Chaudhry
Keyword(s):  
Size Distribution ◽  
Waiting Time ◽  
Queueing Systems ◽  
Queueing Models ◽  
Queue Size ◽  
Different Types

This paper brings out relations among the moments of various orders of the waiting time and the queue size in different types of bulk queueing models.

Simple approximations to the expected waiting time for a cluster of any given size, for point processes

1983 ◽  
Vol 15 (01) ◽  
pp. 21-38 ◽  
Author(s):  
Ester Samuel-Cahn
Keyword(s):  
Waiting Time ◽  
Point Processes ◽  
Upper Bounds ◽  
Poisson Processes ◽  
Lower And Upper Bounds ◽  
Compound Poisson ◽  
Compound Poisson Processes ◽  
Interarrival Times ◽  
Expected Waiting Time ◽  
Simple Points

For point processes, such that the interarrival times of points are independently and identically distributed, let T(L, m) denote the time until at least points cluster within an interval of length at most L. Let τ (L, m) + 1 be the total number of points observed until the above happens. Simple approximations of Eτ (L, m) and ET(L, m) are derived, as well as lower and upper bounds for their value. Approximations to the variances are also given. In particular the Poisson, Bernoulli and compound Poisson processes are discussed in detail. Some numerical tables are included.

A Determinant Identity Implying the Lagrange–Good Inversion Formula

2016 ◽  
Vol 60 (1) ◽  
pp. 165-176
Author(s):  
Jianfeng Huang ◽  
Xinrong Ma
Keyword(s):  
Simple Proof ◽  
Inversion Formula ◽  
Discrete Analogue

AbstractIn this paper a determinant identity is established, from which a simple proof of the multivariate Lagrange–Good inversion formula follows directly. Further discussion on a discrete analogue of the Lagrange–Good inversion formula is also presented.

Correlation functions in queueing theory

1972 ◽  
Vol 9 (3) ◽  
pp. 604-616 ◽  
Author(s):  
S. K. Srinivasan ◽  
R. Subramanian ◽  
R. Vasudevan
Keyword(s):  
Waiting Time ◽  
Correlation Functions ◽  
Queueing Theory ◽  
Product Space ◽  
Point Processes ◽  
Time Interval ◽  
Important Criterion ◽  
Time Parameters ◽  
Set Up ◽  
Number Of Customers

The object of this paper is to study the actual waiting time of a customer in a GI/G/1 queue. This is an important criterion from the viewpoint of both the customers and the efficient functioning of the counter. Suitable point processes in the product space of load and time parameters for any general inter-arrival and service time distributions are defined and integral equations governing the correlation functions are set up. Solutions of these equations are obtained and with the help of these, explicit expressions for the first two moments of the number of customers who have waited for a time longer than w in a given time interval (0, T) are calculated.

A Unified Approach to Linear Equating for the Nonequivalent Groups Design

2005 ◽  
Vol 30 (3) ◽  
pp. 313-342 ◽  
Author(s):  
Alina A. von Davier ◽  
Nan Kong
Keyword(s):  
General Formula ◽  
Standard Error ◽  
Unified Approach ◽  
Unified Framework ◽  
Neat Design ◽  
Nonequivalent Groups ◽  
Standard Error Of Equating ◽  
Observed Score ◽  
Special Case ◽  
Linear Equating

This article describes a new, unified framework for linear equating in a non-equivalent groups anchor test (NEAT) design. The authors focus on three methods for linear equating in the NEAT design—Tucker, Levine observed-score, and chain—and develop a common parameterization that shows that each particular equating method is a special case of the linear equating function in the NEAT design. A new concept, the method function, is used to distinguish among the linear equating functions, in general, and among the three equating methods, in particular. This approach leads to a general formula for the standard error of equating for all linear equating functions in the NEAT design. A new tool, the standard error of equating difference , is presented to investigate if the observed difference in the equating functions is statistically significant.

scholarly journals Identification of waiting time distribution ofM/G/1,Mx/G/1,GIr/M/1queueing systems

1988 ◽  
Vol 11 (3) ◽  
pp. 589-597
Author(s):  
A. Ghosal ◽  
S. Madan
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing System ◽  
Numerical Study ◽  
Queueing Models ◽  
Single Server ◽  
Waiting Time Distribution ◽  
System A ◽  
Bulk Arrival

This paper brings out relations among the moments of various orders of the waiting time of the1st customer and a randomly selected customer of an arrival group for bulk arrivals queueing models, and as well as moments of the waiting time (in queue) forM/G/1queueing system. A numerical study of these relations has been developed in order to find the(β1,β2)measures of waiting time distribution in a comutable form. On the basis of these measures one can look into the nature of waiting time distribution of bulk arrival queues and the single serverM/G/1queue.

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.

COMPLEXITY OF SEMIGROUP IDENTITY CHECKING

2004 ◽  
Vol 14 (04) ◽  
pp. 455-464 ◽  
Author(s):  
ANDRZEJ KISIELEWICZ
Keyword(s):  
Computational Complexity ◽  
General Formula ◽  
Commutative Semigroup ◽  
Simple Proof ◽  
Finite Semigroup ◽  
Structure Theory ◽  
Semigroup Identity ◽  
Commutative Semigroups ◽  
Complexity Status ◽  
Np Complete

We consider the [Formula: see text] problem, whose instance is a finite semigroup S and an identity I, and the question is whether I is satisfied in S. We show that the question concerning computational complexity of this problem is much harder, when restricted to commutative semigroups. We provide a relatively simple proof that in general the problem is co-NP-complete, and demonstrate, using some structure theory, that for a fixed commutative semigroup the problem can be solved in polynomial time. The complexity status of the general [Formula: see text] problem remains open.

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