Computational algorithms for blocking probabilities in circuit-switched networks

Pinsky, Eugene; Conway, Adrian E.

doi:10.1007/bf02023089

Cited by 30 publications

(11 citation statements)

References 21 publications

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“…The product form expression involves a normalizing constant, from which the blocking probability can be determined directly, without needing to determine specific state probabilities. It can be evaluated exactly by recursive methods [Dziong and Roberts 1987;Pinsky and Conway 1992], mean value analysis [Reiser and Lavenberg 1980], generating function inversion methods [Choudhury et al 1995] or uniform asymptotic approximation [Mitra and Morrison 1994]. However, these techniques all have exponential complexity in the number of cells.…”

Section: Introductionmentioning

confidence: 99%

Estimation of blocking probabilities in cellular networks with dynamic channel assignment

Vázquez-Abad

Andrew

Everitt

2002

ACM Trans. Model. Comput. Simul.

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Blocking probabilities in cellular mobile communication networks using dynamic channel assignment are hard to compute for realistic sized systems. This computational difficulty is due to the structure of the state space, which imposes strong coupling constraints amongst components of the occupancy vector. Approximate tractable models have been proposed, which have product form stationary state distributions. However, for real channel assignment schemes, the product form is a poor approximation and it is necessary to simulate the actual occupancy process in order to estimate the blocking probabilities.Meaningful estimates of the blocking probability typically require an enormous amount of CPU time for simulation, since blocking events are usually rare. Advanced simulation approaches use importance sampling (IS) to overcome this problem. In this article, we study two regimes under which blocking is a rare event: low-load and high cell capacity. Our simulations use the standard clock (SC) method. For low load, we propose a change of measure that we call static ISSC, which has bounded relative error. For high capacity, we use a change of measure that depends on the current state of the network occupancy. This is the dynamic ISSC method. We prove that this method yields zero variance estimators for single clique models, and we empirically show the advantages of this method over naïve simulation for networks of moderate size and traffic loads.

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Section: Introductionmentioning

confidence: 99%

Estimation of blocking probabilities in cellular networks with dynamic channel assignment

Vázquez-Abad

Andrew

Everitt

2002

ACM Trans. Model. Comput. Simul.

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“…In [23], the determination of G(P − p k b l , M − b l ) (and consequently the determination of CBP via (2)) is based on the algorithms of [39,40]. These algorithms were initially proposed for the CBP calculation in circuit-switched networks [41,42].…”

Section: The P-s Multirate Loss Model-a Reviewmentioning

confidence: 99%

“…These algorithms were initially proposed for the CBP calculation in circuit-switched networks [41,42]. The algorithms of [39] are based on mean-value analysis and z-transforms. The algorithm of [40] is based on the quite complex approach of numerical inversion of generating functions [43].…”

Section: The P-s Multirate Loss Model-a Reviewmentioning

confidence: 99%

An Analytical Framework in OFDM Wireless Networks Servicing Random or Quasi-Random Traffic

et al. 2019

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We consider the downlink of an orthogonal frequency division multiplexing (OFDM)-based cell that services calls from many service-classes. The call arrival process is random (Poisson) or quasi-random, i.e., calls are generated by an infinite or a finite number of sources, respectively. In order to determine congestion probabilities and resource utilization, we model the cell as a multirate loss model. Regarding the call admission, we consider the restricted accessibility, the bandwidth reservation (BR), and the complete sharing (CS) policies. In a system of restricted accessibility, a new call may be blocked even if resources do exist. In a BR system, subcarriers can be reserved in favor of calls of high subcarrier requirements. Finally, in a CS system, a new call is blocked due to resource unavailability. In all three policies, we show that there exist recursive formulas for the determination of the various performance measures. Based on simulation, the accuracy of the proposed formulas is found to be quite satisfactory.

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“…The conclusion was that condition (S) holds in all the cases considered, for any given set of parameters. To compute the non-blocking probabilities, we used the normalization constant algorithm in Pinsky and Conway [14]. We chose this general algorithm instead of a specialized routine for a tree network (such as Ross and Tsang [16]) because it can easily handle numerical overflows which occur frequently even for mid-size instances.…”

Section: Numerical Analysismentioning

confidence: 99%

Optimal static pricing for a tree network

Caro

Simchi‐Levi

2012

Ann Oper Res

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We study the static pricing problem for a network service provider in a loss system with a tree structure.In the network, multiple classes share a common inbound link and then have dedicated outbound links.The motivation is from a company that sells phone cards and needs to price calls to different destinations.We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.

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Computational algorithms for blocking probabilities in circuit-switched networks

Cited by 30 publications

References 21 publications

Estimation of blocking probabilities in cellular networks with dynamic channel assignment

Estimation of blocking probabilities in cellular networks with dynamic channel assignment

An Analytical Framework in OFDM Wireless Networks Servicing Random or Quasi-Random Traffic

Optimal static pricing for a tree network

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