Blocking Probability Rate Research Articles

Applying Fast Simulation to the Evaluation of Customer Blocking Probability in the Multichannel Queuing System with Multicast Access

Applying Fast Simulation to the Evaluation of Customer Blocking Probability in the Multichannel Queuing System with Multicast Access

Integrating teletraffic theory with neural networks for quality-of-service evaluation in mobile networks

In mobile cellular design, one important quality-of-service metric is the blocking probability. Using computer simulation for studying blocking probability is quite time-consuming, whereas existing teletraffic-based methods such as the Information Exchange Surrogate Approximation (IESA) only give a rough estimate of blocking probability. Another common approach, direct blocking probability evaluation using neural networks (NN), performs poorly when extrapolating to network conditions outside of the training set. This paper addresses the shortcomings of existing teletraffic and NN-based approaches by combining both approaches, creating what we call IESA-NN. In IESA-NN, an NN is used to estimate a tuning parameter, which is in turn used to estimate the blocking probability via a modified IESA approach. In other words, the teletraffic approach IESA still forms the core of IESA-NN, with NN techniques used to improve the accuracy of the approach via the tuning parameter. Simulation results show that IESA-NN performs better than previous approaches based on NN or teletraffic theory alone. In particular, even when the NN cannot produce a good value for the tuning parameter, for example when extrapolating to network conditions not experienced in the training set, the final IESA-NN estimate is generally still accurate as the estimate is primarily determined by the underlying teletraffic theory, with the NN determining the tuning parameter playing a supplementary role. The combination of the IESA framework with NN in a secondary role makes IESA-NN quite robust.

A Century-Long Challenge in Teletraffic Theory: Blocking Probability Evaluation for Overflow Loss Systems With Mutual Overflow

A Century-Long Challenge in Teletraffic Theory: Blocking Probability Evaluation for Overflow Loss Systems With Mutual Overflow

Evaluation of Network Blocking Probability and Network Utilization Efficiency on Proposed Elastic Optical Network using RSA Algorithms

AbstractElastic optical networks (EONs) are new generation optical networks that provide flexible bandwidth and spectrum assignment characteristics to accommodate diverse demand range over traditional dense wavelength division multiplexing (DWDM)-based networks. While overcoming spectrum contiguity and continuity constraints, Routing and Spectrum Assignment (RSA) is a challenging task in EONs. In this article, we have proposed an EON network model. Using existing RSA techniques we have analyzed the performance of the proposed model on the basis of Network Blocking Probability (NBP) and Network Utilization Efficiency (NUE) under variable load conditions. It has been found to be working optimally even at a load of 200 Erlangs.

Blocking Probability Evaluation for Non-Hierarchical Overflow Loss Systems

Non-hierarchical overflow loss systems (NH-OLSs) with mutual overflow have applications in many telecommunications and service systems, e.g., cellular networks, video-on-demand, emergency healthcare, or cloud services. In this paper, we make fundamental contributions in teletraffic modeling for blocking probability evaluation in NH-OLSs. These are based on the development of the well-known decomposition methodology, which decomposes an NH-OLS into independent subsystems and applies a suitable node model to each subsystem. In particular, we provide new both theoretical and numerical results involving both new and existing approximation methods. We show that these results cover a broad range of NH-OLSs, including those with heterogeneous arrival processes, server group size, and/or routing, with both Poisson and non-Poisson arrivals of fresh requests. Our theoretical results include the first scalable asymptotic exactness results for NH-OLSs. Our new approximations include the first computationally efficient and fairly accurate approximation for NH-OLSs with both mutual overflow and non-Poisson input with asymptotic exactness properties.

Extreme Learning Machine for Estimating Blocking Probability of Bufferless OBS/OPS Networks

Recently, the neural network approach for the blocking probability evaluation on optical networks was proposed, in which the inputs of the neural network were the optical network parameters and the output was the blocking probability of the optical network. The numerical results showed that its evaluation speed of the blocking probability was thousands of times faster than that of the discrete event simulator. However, the existing approach had two drawbacks. First, when the blocking probability was small, there was a significant approximation error due to the high dynamic range of the blocking probability. Second, the single-hidden-layer feedforward network model was used, which needed some time-consuming training algorithms to learn the parameters of hidden nodes, such as backpropagation. To solve these problems, this paper proposes to use the mean squared error of the log blocking probability as the training objective and use the extreme learning machine (ELM) framework for the training. Our numerical results show that the blocking probability estimated by our training objective is much more accurate than that of the existing approach, and it is obtained efficiently due to the greatly simplified training procedure offered by the ELM.

Surrogate models for performance evaluation of multi-skill multi-layer overflow loss systems

We consider a model of overflow loss systems in which server groups are arranged into layers, and alternate routing within each layer creates mutual overflow effects, increasing the amount of traffic that can be carried by the system. Such a model has wide applications in communications and service systems. However, the presence of both hierarchical inter-layer overflow and mutual intra-layer overflow makes accurate, robust, yet scalable blocking probability evaluation of such systems a difficult challenge. To address this challenge, we apply and extend the recently developed Information Exchange Surrogate Approximation (IESA) framework to a multi-layer system, adding new surrogate models to the framework and incorporating moment-matching techniques. In contrast to the conventional fixed-point approximation (FPA) approach, which directly decomposes the overflow loss system into independent subsystems with inherent problems of convergence and uniqueness, IESA performs decomposition on a carefully designed surrogate model with guaranteed convergence and uniqueness. Extensive numerical results demonstrate that IESA is consistently more accurate than the conventional FPA approach, showing an improvement in accuracy of several orders of magnitude in many cases. Furthermore, the new extensions to IESA introduced in this paper provide consistent improvements in accuracy relative to the current state-of-the-art of the IESA framework.

Evaluation of Blocking Probability for Downlink in Poisson Networks

In recent years, wireless network modeling using stochastic geometry tools, like Poisson Point Process (PPP), has acquired the attention of researchers. Modeling of interference, coverage, and capacity for cellular networks using PPP is presented in literature. However, the blocking probability remains to be investigated. In this letter, we present an analytical framework for evaluation of network blocking probability for downlink. The services can be categorized using multiple classes based on the average resource units required by the service. The multi-class service scenario is modeled using multi-dimensional Markov Chain. The Markov chain is further approximated using the Erlang approximation method to evaluate the activity factor of a base station (BS). Moreover, an approximate closed form expression for coverage probability is derived, which is applicable to interference as well as noise limited scenario. Exploiting the coupling between coverage and activity factor, we determine the class-wise arrival rate. Further, the class-wise arrival rates are used to determine the networks blocking probability. We validate the proposed analytical framework through the extensive simulation.

SIMTON: A Simulator for Transparent Optical Networks DOI: 10.14209/jcis.2010.1

In this article we present a software to simulate Transparent Optical Networks (SIMTON). SIMTON is an eventdriven simulation software implemented in C++ which takes into account optical device characteristics for the evaluation of network blocking probability in wavelength routed transparent optical networks. The simulator uses a physical layer model that considers the following effects: device losses, fiber attenuation, four wave mixing, residual chromatic dispersion and polarization mode dispersion in optical fibers, gain saturation in optical amplifiers (Erbium Doped Fiber Amplifier), dependence of the amplified spontaneous emission noise with the input power in EDFA, in-band crosstalk in optical switches, and source spontaneous emission noise of the laser transmitter. By using SIMTON it is possible to adjust the parameters of the optical devices, as well as to choose the routing and wavelength assignment algorithm. Moreover, the tool has a graphical interface. We also present some examples of network analysis results obtained from SIMTON.

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.

Blocking probability evaluation of end-to-end dynamic WDM networks

Two mathematical methods for blocking probability evaluation of end-to-end dynamic WDM networks are proposed. The first method can be applied to networks operating with static (fixed) routes. By diminishing the impact of the link independence assumption, the method proposed improves a recently proposed mathematical procedure that assumes link blocking independency and non-Poisson traffic. To do so, the so-called streamline effect is taken into account in the equations. As a result, values closer to that of simulation are obtained. The second method applies to networks operating with alternate routing. In this case, the method simultaneously relaxes three non-realistic assumptions of previous works: the link blocking independence, the Poisson traffic arrival and the homogeneity of the traffic load offered to the network links. Both methods were applied to different network topologies, and their results were compared to those of simulation. Results show that the match between simulation and the proposed methods is excellent, and better than assuming link blocking independence, in all the topologies studied.

Performance analysis of OBS networks using the effective bandwidth method

This article provides a new scheme for the blocking probability evaluation for optical burst switching networks. While several previous articles used mainly links as servers, we consider switches as servers. In order to evaluate the blocking probability at switches, we use the effective bandwidth method. The method shows more accurate results and the accuracy of the method is proven by simulation and numerical analyses.

A New Method for Blocking Probability Evaluation in OBS/OPS Networks With Deflection Routing

In this paper, we present a new method for the estimation of blocking probabilities in bufferless optical burst or packet switched networks. In such networks, deflection routing is used to reduce blocking probability. However, it requires certain wastage due to trunk reservation that must be used to avoid instability. We provide a wide range of simulation and numerical results to validate our new approximation method and demonstrate various effects on blocking probability and utilization, such as network size, trunk size, the maximal number of allowable deflections, and burst/packet length.

Enhanced Blocking Probability Evaluation Method for Circuit-Switched Trunk Reservation Networks

We consider the problem of estimating steady-state blocking probability for circuit-switched networks that allow alternate routing with particular emphasis on networks protected by trunk reservation. We use a recently proposed blocking probability estimate, the Overflow Priority Classification Approximation (OPCA) as an alternative to the currently used Erlang's Fixed-Point Approximation (EFPA). We demonstrate empirically that OPCA provides a better blocking estimate than EFPA for circuit-switched networks with alternate routing, that are reasonably protected by trunk reservation.

On Generalizations of the Engset Model

The Engset model has been extensively studied and widely used for blocking probability evaluation in telecommunications networks. In 1957, J.W. Cohen considered two generalizations of the Engset model: 1) permitting the distributions of the holding time and interarrival time to differ from source to source; 2) permitting the idle time distribution to depend on whether or not the previous call was successful. He derived the call and time congestions for the first generalization, however, he simply posed the second generalization as a problem. In a leading teletraffic text by Syski, the call and time congestions are approximated for the second generalization, though it appears that Syski has overlooked that his results are in fact an approximation. In this paper, we point out Syski's apparent oversight, we improve the accuracy of his approximation, and we provide an efficient algorithm for its numerical computation and prove its convergence

Fast blocking probability evaluation of end-to-end optical burst switching networks with non-uniform ON–OFF input traffic model

A novel, accurate, numerically stable and fast mathematical method for network-wide blocking probability evaluation of end-to-end optical burst switching (OBS) networks with heterogeneous link capacity under non-uniform traffic is proposed. Unlike most of previous works, which have used the Poisson model for the burst traffic, this paper considers a non-uniform ON–OFF model being a more realistic choice for OBS networks. Compared with simulation, the method was proved to be very accurate and much faster (up to four orders of magnitude faster than simulation in the studied cases). These features make the proposed method very useful for network analysis, especially for large size networks where simulation time can be prohibitively high.

An analytical model for CDMA downlink rate optimization taking into account uplink coverage restrictions

This paper models and analyzes downlink and uplink power assignment in code division multiple access (CDMA) mobile networks. By discretizing the area into small segments, the power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression of the so-called Perron–Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for each distribution of calls over the segments. Our results allow for a fast evaluation of outage and blocking probabilities. The result also enables a quick evaluation of feasibility that may be used for capacity allocation. Our combined downlink and uplink feasibility model is applied to determine maximal system throughput in terms of downlink rates.

Blocking Probability Approximations and Revenue Optimization in Multirate Loss Networks

For the end-to-end (Originator-Destination pair) call blocking probability computation in multirate loss networks the so-called reduced load approximation under link independence assumption is often used, because it allows the derivation of analytical and numerical results. Its accuracy and extendibility to multirouting or multicasting networks (like me B-ISDN), however, is seldom studied. This paper attempts to generalize this assumption and to assess the usefulness of this generalization by comparing simulation and approximation results on link, route, and end-to-end blocking probability evaluation for these kinds of networks. The accuracy of the approximation is examined by a simulation tool called Flexible Simulation Platform for ATM Networks. An important application example of this generalized link-, route- and Originator-Destination pair blocking measure is the formulation of an optimization model for multirate loss networks, which optimizes carried traffic and network revenue.

Time-division switching networks with partial-access pulse shifters performing serial-parallel conversion

Some means of time-slot interchanging is required in a pulse-code-modulation (PCM) transit switching system to satisfy the blocking requirements due to the fact that average trunk loading is high and that the time slots of incoming calls are preassigned at the remote office. This paper presents the use of serial-to-parallel conversion and parallel-to-serial conversion pulse shifters, both having limited time-slot interchange capability at the input and the output of the switching networks, respectively. The features of the system are that the required memory capacity is much smaller than the conventional systems and that serial transmission and parallel switching are possible. The results of optimization through blocking probability evaluation and network cost estimation are also described for networks with one, two, and three gate stages, and with an additional parallel pulse-shifter stage.