Asymptotic Blocking Probabilities in Loss Networks with Subexponential Demands

The analysis of stochastic loss networks has long been of interest in computer and communications networks and is becoming important in the areas of service and information systems. In traditional settings computing the well-known Erlang formula for blocking probabilities in these systems becomes intractable for larger resource capacities. Using compound point processes to capture stochastic variability in the request process, we generalize existing models in this framework and derive simple asymptotic expressions for the blocking probabilities. In addition, we extend our model to incorporate reserving resources in advance. Although asymptotic, our experiments show an excellent match between derived formulae and simulation results even for relatively small resource capacities and relatively large values of the blocking probabilities.

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Information Systems Outsourcing in Large Companies

Computer Engineering ◽

10.4018/978-1-61350-456-7.ch612 ◽

2012 ◽

pp. 1554-1568

Author(s):

Mark Leeney ◽

João Varajão ◽

António Trigo Ribeiro ◽

Ricardo Colomo-Palacios

Keyword(s):

Project Management ◽

Information Systems ◽

Software Development ◽

Focus Attention ◽

Communications Networks ◽

Republic Of Ireland ◽

The Past ◽

Wide Range ◽

The Republic ◽

Indispensable Tool

Information systems outsourcing is an indispensable tool in the management of information systems. The set of services contracted to outside suppliers, originally more limited to services of an operational nature, has expanded over the past two decades, and today there is a wide range of services subject to outsourcing. Among them are: the hiring of software development; maintenance of applications; services and communications networks; security of information systems; and many others. Depending on the nature of the services contracted and on the range that the contracting of services has on departments of information systems, the issues involved in project management vary considerably. This article presents the results of a survey conducted among large companies in the Republic of Ireland to characterize, among other things, the range of services that are most often outsourced. The results are relevant in the sense that not only do they enable a better understanding of the reality of information systems departments of large Irish companies, but also enable the management to focus attention on specific services.

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Limit theorems for loss networks with diverse routing

Advances in Applied Probability ◽

10.1017/s0001867800019066 ◽

1989 ◽

Vol 21 (04) ◽

pp. 804-830 ◽

Cited By ~ 1

Author(s):

I. B. Ziedins ◽

F.P. Kelly

Keyword(s):

Information Systems ◽

Asymptotic Analysis ◽

Limit Theorems ◽

Loss Networks ◽

Exact Analysis ◽

Large Numbers

Loss networks have long been of interest to telephone engineers, and are becoming increasingly important as models of computer and information systems. In this paper we present an asymptotic analysis of loss networks exhibiting various forms of symmetry. Our aim is to better understand the behaviour of networks involving very large numbers of links and routes, where an exact analysis is not possible and approximations are required.

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Blocking probabilities for large multirate erlang loss systems

Advances in Applied Probability ◽

10.1017/s0001867800025866 ◽

1993 ◽

Vol 25 (04) ◽

pp. 997-1009 ◽

Cited By ~ 4

Author(s):

Pawel Gazdzicki ◽

Ioannis Lambadaris ◽

Ravi R. Mazumdar

Keyword(s):

Large Deviations ◽

Unified Framework ◽

Blocking Probabilities ◽

Asymptotic Expressions ◽

Loss Systems ◽

Heavy Loads ◽

Erlang Loss

This paper is concerned with the computation of asymptotic blocking probabilities for a generalized Erlangian system which results when M independent Poisson streams of traffic with rates access a trunk group of C circuits with traffic from stream k requiring Ak circuits which are simultaneously held and released after a time which is randomly distributed with unit mean and independent of earlier arrivals and holding times. A call from stream k is lost if on arrival less than Ak circuits are available. Although exact expressions for the blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the switch increases in that both the traffic rates and trunk capacity are scaled together, simple asymptotic expressions for the blocking probabilities are obtained. In particular the expression is different for light, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysis.

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A class of interacting marked point processes: rate of convergence to equilibrium

Journal of Applied Probability ◽

10.1239/jap/1019737994 ◽

2002 ◽

Vol 39 (1) ◽

pp. 137-160 ◽

Cited By ~ 2

Author(s):

G. L. Torrisi

Keyword(s):

Stochastic Processes ◽

Rate Of Convergence ◽

Point Processes ◽

Marked Point ◽

Marked Point Processes ◽

Convergence To Equilibrium ◽

Birth And Death Processes ◽

Loss Networks

In this paper we obtain the rate of convergence to equilibrium of a class of interacting marked point processes, introduced by Kerstan, in two different situations. Indeed, we prove the exponential and subexponential ergodicity of such a class of stochastic processes. Our results are an extension of the corresponding results of Brémaud, Nappo and Torrisi. The generality of the dynamics which we take into account allows the application to the so-called loss networks, and multivariate birth and death processes.

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ASYMPTOTIC EVALUATION OF BLOCKING PROBABILITIES IN A HIERARCHICAL CELLULAR MOBILE NETWORK

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800141075 ◽

2000 ◽

Vol 14 (1) ◽

pp. 81-99 ◽

Cited By ~ 1

Author(s):

Stefan Verwijmeren ◽

Michel Mandjes ◽

Richard J. Boucherie

Keyword(s):

Large Deviations ◽

Mobile Communications ◽

Mobile Network ◽

State Spaces ◽

Communications Networks ◽

Blocking Probabilities ◽

Asymptotic Evaluation ◽

Cellular Mobile ◽

Efficient Approximation ◽

Cellular Mobile Network

This paper investigates blocking probabilities obtained from multidimensional truncated Poisson distributions. For blocking probabilities typically arising in layered cellular mobile communications networks, the large deviations results of Gazdzicki et al. [9] are extended to state spaces determined by multiple constraints. The results yield asymptotically exact expressions that provide an accurate approximation of probabilities up to 1%, which considerably extends the applicability of large deviations results and enables efficient approximation of blocking probabilities for realistic mobile communications networks.

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Blocking probabilities for large multirate erlang loss systems

Advances in Applied Probability ◽

10.2307/1427803 ◽

1993 ◽

Vol 25 (4) ◽

pp. 997-1009 ◽

Cited By ~ 34

Author(s):

Pawel Gazdzicki ◽

Ioannis Lambadaris ◽

Ravi R. Mazumdar

Keyword(s):

Large Deviations ◽

Unified Framework ◽

Blocking Probabilities ◽

Asymptotic Expressions ◽

Loss Systems ◽

Heavy Loads ◽

Erlang Loss

This paper is concerned with the computation of asymptotic blocking probabilities for a generalized Erlangian system which results when M independent Poisson streams of traffic with rates access a trunk group of C circuits with traffic from stream k requiring Ak circuits which are simultaneously held and released after a time which is randomly distributed with unit mean and independent of earlier arrivals and holding times. A call from stream k is lost if on arrival less than Ak circuits are available. Although exact expressions for the blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the switch increases in that both the traffic rates and trunk capacity are scaled together, simple asymptotic expressions for the blocking probabilities are obtained. In particular the expression is different for light, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysis.

Download Full-text

Information Systems Outsourcing in Large Companies

International Journal of Information Technology Project Management ◽

10.4018/jitpm.2011100104 ◽

2011 ◽

Vol 2 (4) ◽

pp. 44-58 ◽

Cited By ~ 9

Author(s):

Mark Leeney ◽

João Varajão ◽

António Trigo Ribeiro ◽

Ricardo Colomo-Palacios

Keyword(s):

Project Management ◽

Information Systems ◽

Software Development ◽

Focus Attention ◽

Communications Networks ◽

Republic Of Ireland ◽

The Past ◽

Wide Range ◽

The Republic ◽

Indispensable Tool

Information systems outsourcing is an indispensable tool in the management of information systems. The set of services contracted to outside suppliers, originally more limited to services of an operational nature, has expanded over the past two decades, and today there is a wide range of services subject to outsourcing. Among them are: the hiring of software development; maintenance of applications; services and communications networks; security of information systems; and many others. Depending on the nature of the services contracted and on the range that the contracting of services has on departments of information systems, the issues involved in project management vary considerably. This article presents the results of a survey conducted among large companies in the Republic of Ireland to characterize, among other things, the range of services that are most often outsourced. The results are relevant in the sense that not only do they enable a better understanding of the reality of information systems departments of large Irish companies, but also enable the management to focus attention on specific services.

Download Full-text

A new method to determine blocking probabilities in micro- and picocellular wireless communications networks

GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record ◽

10.1109/glocom.1997.638478 ◽

2002 ◽

Cited By ~ 3

Author(s):

S. Mayer

Keyword(s):

Wireless Communications ◽

New Method ◽

Communications Networks ◽

Blocking Probabilities

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Fixed Point Approximations for Retrial Networks

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800004319 ◽

1996 ◽

Vol 10 (2) ◽

pp. 243-259 ◽

Cited By ~ 2

Author(s):

Glen K. Takahara

Keyword(s):

Fixed Point ◽

Network Models ◽

Independence Assumption ◽

Loss Networks ◽

Blocking Probabilities ◽

Rate Limit

Fixed point approximations for blocking probabilities arising from a link independence assumption and a light retrial rate limit are derived for circuitswitched network models that incorporate caller retrials. This approximation is a generalization of the well-known reduced load approximation for loss networks, which retains much of the versatility of this approximation.

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