The Reliability of Telephone Traffic Load Measurements by Switch Counts

Hayward, WG

doi:10.1002/j.1538-7305.1952.tb01386.x

Cited by 11 publications

(3 citation statements)

References 2 publications

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“…Hence, one has to rely on approximations in order to estimate the blocking probability in overflow loss queues. In this paper we use the approximation proposed by Hayward [13], [14], which tries to describe non Poisson traffic by means of equivalent Poisson traffic, and then apply the usual Erlang-B formula for estimating the blocking probability. Both served and overflow traffic have properties which differ from the the system where the two queues are isolated; however it can be classified according to its peakedness Z (a measure of the traffic variability), which is defined as the ratio between the variance and the mean of the number of busy servers in infinite servers queue (see [11] for more details).…”

Section: B Throughput Estimationmentioning

confidence: 99%

Reserved or On-Demand Instances? A Revenue Maximization Model for Cloud Providers

Mazzucco

Dumas

2011

2011 IEEE 4th International Conference on Cloud Computing

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Abstract-We examine the problem of managing a server farm in a way that attempts to maximize the net revenue earned by a cloud provider by renting servers to customers according to a typical Platform-as-a-Service model. The Cloud provider offers its resources to two classes of customers: 'premium' and 'basic'. Premium customers pay upfront fees to reserve servers for a specified period of time (e.g. a year). Premium customers can submit jobs for their reserved servers at any time and pay a fee for the server-hours they use. The provider is liable to pay a penalty every time a 'premium' job can not be executed due to lack of resources. On the other hand, 'basic' customers are served on a best-effort basis, and pay a server-hour fee that may be higher than the one paid by premium customers. The provider incurs energy costs when running servers. Hence, it has an incentive to turn off idle servers. The question of how to choose the number of servers to allocate to each pool (basic and premium) is answered by analyzing a suitable queuing model and maximizing a revenue function. Experimental results show that the proposed scheme adapts to different traffic conditions, penalty levels, energy costs and usage fees.

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Section: B Throughput Estimationmentioning

confidence: 99%

Reserved or On-Demand Instances? A Revenue Maximization Model for Cloud Providers

Mazzucco

Dumas

2011

2011 IEEE 4th International Conference on Cloud Computing

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“…Statistical aspects of the sampling techniques used in traffic measurement were analyzed by Wilkinson (1941), John Riordan (1951), Hayward (1952), Václav E. Beneš (1961), Alfred Descloux (1965Descloux ( , 1976, and others. Tables of traffic system behavior were published by Molina (1927), Riordan (1953), Wilkinson (1953Wilkinson ( , 1970, Paul J.…”

Section: Traffic Variabilitymentioning

confidence: 99%

Operations Research at Bell Laboratories Through the 1970s: Part I

Dawson¹,

McCallum²,

Murphy³

et al. 2000

Operations Research

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This historical account of operations research at Bell Laboratories was drafted in the late 1970s when the authors were part of the Operations Research Center within Bell Laboratories at AT&T; it has not previously appeared in the open literature. We have added a few references to later publications that describe particular aspects of the period covered. Discussions of technological practices and organizational arrangements expressed in the present tense represent a viewpoint of about 1980, before “divestiture” split up the Bell System. The principal topics in this issue of Operations Research are the organizational history, and teletraffic theory and engineering. Upcoming issues of Operations Research will include parts II and III of this account, comprising capacity expansion in telephone networks, operations analysis, applied statistics, and related OR activities. A comprehensive table of contents for parts I, II, and III can be found in the Online Collection of the Operations Research Home Page, at www.informs.org/pubs .

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“…is a random step-function fluctuating in unit steps between°and N. As is well known, N(·) has stationary probabilities {Pn, n = 0,1,"', Nl given by the (first) Erlang distribution (1) = equilibrium probability that n trunks are busy.…”

Section: These Assumptions Determine a Markov Stochastic Process N(t)mentioning

confidence: 99%

The Covariance Function of a Simple Trunk Group, with Applications to Traffic Measurement*

Beneš¹

1961

Bell System Technical Journal

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Erlang's classical model for telephone traffic in a loss system is considered: N trunks, calls arriving in a Poisson process and negative exponential holding times; calls which cannot be served at once are dismissed without retrials. Let N(t) be the number of trunks in use at t. An explicit formula for the covariance R(·) of N(·) in terms of the characteristic values of the transition matrix of the Markov process N ( .) is obtained. Also, R(·) is expressed purely in terms of constants and the "recovery"function, i.e. the transition probability PrIN(t) is accurately approximated by R(O)e'II, with rl the largest negative characteristic value, itself well appro:r:imated (underestimated) by -EIN(· )}/ R(O). Exact and approximate formulas for sampling error in traffic measurement are deduced from these results.

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The Reliability of Telephone Traffic Load Measurements by Switch Counts

Abstract: The switch count method of telephone traffic measurement is subject to sampling errors. The nature of these errors is discussed and formulas are derived which describe the extent of the errors under normally encountered traffic conditions.

Cited by 11 publications

References 2 publications

Reserved or On-Demand Instances? A Revenue Maximization Model for Cloud Providers

Reserved or On-Demand Instances? A Revenue Maximization Model for Cloud Providers

Operations Research at Bell Laboratories Through the 1970s: Part I

The Covariance Function of a Simple Trunk Group, with Applications to Traffic Measurement*

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