Blocking Probability Approximation Research Articles

Blocking performance approximation in flexi-grid networks

Abstract The blocking probability to the path requests is an important issue in flexible bandwidth optical communications. In this paper, we propose a blocking probability approximation method of path requests in flexi-grid networks. It models the bundled neighboring carrier allocation with a group of birth–death processes and provides a theoretical analysis to the blocking probability under variable bandwidth traffic. The numerical results show the effect of traffic parameters to the blocking probability of path requests. We use the first fit algorithm in network nodes to allocate neighboring carriers to path requests in simulations, and verify approximation results.

Bounds of the Overflow Priority Classification for Blocking Probability Approximation in OBS Networks: Errata

Bounds of the Overflow Priority Classification for Blocking Probability Approximation in OBS Networks: Errata

Bounds of the Overflow Priority Classification for Blocking Probability Approximation in OBS Networks

It has been demonstrated that the overflow priority classification approximation (OPCA) is an accurate method for blocking probability evaluation for various networks and systems, including optical burst switched networks with deflection routing. OPCA is a hierarchical algorithm that requires fixed-point iterations in each layer of its hierarchy. This may imply a long running time. We prove here that the OPCA iterations alternately produce upper and lower bounds that consistently become closer to each other as more fixed-point iterations in each layer are used, and we demonstrate numerically that only a small number of iterations per layer are required for the bounds to be sufficiently close to each other. This behavior is demonstrated for various system parameters including offered load, number of channels per trunk, and maximum allowable number of deflections.

Computation of Blocking Probability for Large Circuit Switched Networks

The ever-growing Internet and the mounting evidence to the important role of circuit switching motivate the need for an accurate and scalable means for performance evaluation of large circuit switched networks. Previous work has shown that the Erlang Fixed Point Approximation (EFPA) achieves accurate results for such networks where the number of channels (circuits) per link is large. However, a conventional application of EFPA for large networks is computationally prohibitive. In cases where the EFPA solution is unattainable, we propose, in this paper, to use an asymptotic approximation, which we call A-EFPA, for the link blocking probability and demonstrate savings of many orders of magnitudes in computation time for blocking probability approximation in realistically sized networks with large number of circuits per link. We demonstrate for NSFNet and Internet2 accurate calculations of the blocking probability using simulations, EFPA and A-EFPA, where each of these three methods is used for a different range of parameter values.

Modeling an OBS Node under Critical Load and High Utilization Conditions

We consider a bufferless optical burst switching optical cross connect modeled as a continuous-time Markov chain based on a generalized Engset model. We focus specifically on critical load and other given levels of high utilization conditions and evaluate the required number of wavelength channels per cable to keep the blocking probability below a given level. We observe that although a large number of wavelength channels per cable are required to achieve low blocking probability under critical load condition, the required number of such channels decreases significantly if the utilization is allowed to drop to 90% or 80%. We also propose a new blocking probability approximation that is more accurate than previous approximations under critical load condition.

ASYMPTOTIC EVALUATION OF BLOCKING PROBABILITIES IN A HIERARCHICAL 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.

Analytic Approximation of Blocking Probabilities in Circuit Switched Communication Networks

A method inspired from S. Katz's service evaluation algorithm [6] is presented. The new algorithm is recursive, rather than iterative, in nature, and especially suited for networks that do not contain cycles. It also introduces two new features which take existing theoretical results into account, and as such corresponds more closely to the current state of traffic theory.