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

Rapid development of optical communication techniques has made possible large scale wavelength routing optical networks. Nowadays, these networks are deployed worldwide. Large scale networks have natural hierarchies due to either geographical reasons or administrative consideration and are therefore managed in a hierarchical way correspondingly. That is, networks are composed of several subnetworks, which are themselves composed of other even smaller subnetworks. Erlang fixed point approximation (reduced load approximation) has been extensively used in performance evaluation of end to end call blocking probability in traditional circuit switching networks, which are also called loss networks. This method has also been extended for hierarchical loss networks. However, performance evaluation of call blocking probability in hierarchical wavelength routing optical networks has not yet been presented. In this paper, a kind of approximation method is developed for analyzing end to end call blocking probability in hierarchical wavelength routing optical networks. By iteratively running processes combining a top-down load distribution and a bottom-up calculation of node-pair blocking in the network hierarchy, a steady state will be reached and approximate end to end call blocking probability in hierarchical wavelength routing optical network is obtained. Both the link independent model and the link correlation model are used in our analysis. By comparing theoretical results derived from our approximation method and results obtained from discrete event simulation, we illustrate that our method gives reasonable estimate of end to end call blocking probability in hierarchical wavelength routing optical networks, with the correlation model giving much more accurate estimate than the independent model.

The stability of non-hierarchical circuit-switched networks is considered. New results are derived, using the equilibrium flow technique, which relate various parameters to network stability. It is demonstrated that instability is a pervasive phenomenon in networks with mutual overflow, while trunk reservation and route cancellation provide effective means to stabilize an otherwise unstable network. A simple expression is derived for a stabilizing reservation level.

An analysis is made of an alternate-path routing rule called maximum free circuit routing (MFCR). In the use of MFCR, a call is routed to the alternate path that has the maximum number of free circuits when the direct path is blocked. Analytical results show that in conjunction with trunk reservation, this routing rule can offer a stable throughput at high traffic conditions and can increase the call carrying capacity by about 20% (compared to direct path routing) under a blocking requirement of 10/sup -2/ on a fully connected symmetrical nonhierarchical network. >

We investigate a distributed, state-dependent, dynamic routing strategy for circuit-switched loss networks which we have called Aggregated-Least-Busy-Alternative (ALBA). The networks considered are symmetric and fully connected, the offered calls form Poisson streams and routes have at most two links. In ALBA(K), the states of each link are lumped intoK (K ≥ 2) aggregates and the route of each call is determined by local information on the aggregate-states of the links of the alternate routes. The last aggregate is always the set of states reserved for direct traffic and defined by the trunk reservation parameter. The particular case of ALBA in which there is no aggregation is Least-Busy-Alternative (LBA); ALBA(2) represents the other extreme of aggregation. We consider two separate asymptotic scalings based on Fixed Point Models for ALBA(K) which were obtained and investigated in an earlier paper. In the first, it is assumed that the number of network nodes, the offered traffic and trunk group size are all large; their ratios have been chosen to reflect practical interest. The results show that there exists a threshold which delineates fundamentally different behavior: for offered traffic below the threshold, the network loss probability decreases exponentially with increasing network size, while above the threshold the decrease is only polynomial. In the related second asymptotic scaling, the asymptotically optimum trunk reservation parameter is obtained as the solution of a simple equation. Such asymptotically optimal designs are compared to the outputs of exhaustive numerical searches for some realistically sized networks and found to perform very well.

The authors consider integrated data/voice circuit-switched networks which assume a star topology consisting of local area networks (LANs) interconnected through a backbone metropolitan area network (MAN). The stations are classified into two categories: data and voice stations. They are characterized by different arrival rate and session-length (holding time) statistics. A data (voice) session connection between a LAN-i station and a LAN-j station requires the allocation of a dedicated circuit (m circuits for voice) in the underlying LANs (i and j) and an interconnecting circuit (m circuits) in the backbone MAN. End-to-end blocking probabilities are calculated in terms of three components: circuit blocking probability, destination busy probability, and concurrent busy probability. For larger size systems, the authors develop an iterative algorithm that provides a computationally efficient method for the calculation of the end-to-end blocking probabilities. They incorporate into this algorithm the effects of the destination busy events, demonstrating that such events could provide a significant contribution to the end-to-end blocking performance when network conditions induce pronounced destination busy probabilities for all or some stations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spectrum holding per cellular telephony service provider in India is significantly lower than the world average. The spectrum is also severely fragmented across bands and the fragments also have different license conditions. Regulators in India have recently recognized that such spectrum fragmentation is a source of inefficiency for the service providers and have allowed sharing of spectrum among the providers. The genesis of this paper is this regulatory order and it has a three-fold objective. We first study an example spectrum allocation. By assuming GSM-like voice telephony service, we analyse the spectrum holding in one service area in some detail. Using simple calculations, we see that complete pooling of resources by the providers may not be stable-one provider may have a lower blocking probability if it does not form a coalition. This leads us to our second objective of developing analytically tractable partial sharing models where the providers do not pool all their resources. For a probabilistic spectrum sharing model, we analyse a simple system and obtain the partial sharing that will make the coalition stable and Pareto efficient. This model is then extended to a larger system and numerical results from the analytical model are used to obtain additional insights. We then consider a deterministic sharing model for which we also present a similar analysis for this system. We also show that the deterministic sharing system can be analysed via a suitably defined circuit multiplexed network that allows us to use Kelly's Erlang fixed point approximation which in turn provides economic insights. The final objective is to develop a game theoretic model for partial sharing. We provide a Nash bargaining framework for partial sharing. We also discuss some revenue sharing mechanisms when the providers' benefits from partial sharing are asymmetric.

In previous work, we proposed a neural network approach to estimate the blocking probability of optical networks with fixed routing. The neural network was implemented by the extreme learning machine (ELM) framework, in which the training inputs were the optical network parameters, and the output was the overall blocking probability. The numerical results showed that the neural-network-based estimation was accurate and thousands of times faster than a computer simulation. In this paper, we apply the neural network approach to optical circuit switching (OCS) networks with fixed-alternate routing and improve the training method by using an enhancement of ELM framework. Unlike the previous ELM framework, the enhancement of ELM framework provides a random-search-based selection phase for the hidden nodes during the training step. As a result, similar performance can be achieved using fewer hidden nodes than the previous ELM framework. The numerical results show that the new enhancement of ELM training algorithm provides more accurate blocking probability estimates while reducing the required number of hidden nodes by a third compared with the previous ELM training algorithm. Furthermore, for some light traffic loading situations, our new training algorithm is hundreds of times more accurate than the existing well-known analytical approximation method.

In this paper we consider a transmission link of a broadband system. A number of heterogeneous streams with different traffic intensities, different call holding times and different bandwidth requirements use the link in a complete sharing mode with trunk reservation. A normal-type approximation formula for individual blocking probabilities is described. Some numerical examples are presented to show the accuracy of the approximation.

This paper focuses on routing strategies for elastic flows within a flow-based routing architecture. In contrast to other elastic flow routing studies, we assume that elastic flows have a minimum guaranteed rate and are, therefore, subject to admission control. Our ultimate goal is to devise an adaptive algorithm that maximizes the throughput of elastic flows at light load and that preserves network efficiency under overload conditions. To this end, we examine in this paper the impact of trunk reservation on elastic flow quality of service. Trunk reservation is a technique commonly used in circuit-switched networks to prevent performance degradation under overload conditions. Two algorithms integrating a form of trunk reservation are proposed and their performance compared by means of simulation to the performance achieved by an alternative algorithm that we proposed and evaluated in an earlier study [1]. Our results highlight interesting features of trunk reservation when used for elastic flow routing.KeywordsAdmission ControlLight LoadAccess RateBottleneck LinkOverload ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, we investigate the design and performance of multi-path routing in optical wavelength division multiplexed (WDM) networks, that support traffic grooming. A circuit-switched network is considered, where connection requests arriving to the network have to be allotted an end-to-end path carrying the requested bandwidth. Traffic grooming implies that the capacity of a wavelength on a fiber link (e.g. OC-48) will be shared among several lower capacity connections (e.g. OC-3). In order to increase the network performance in terms of improved blocking probability and also to support survivable operation, a connection is split into multiple smaller sub-streams and carried on multiple sub-paths from source to destination. This is based on the Virtual Concatenation (VCAT) mechanisms used in SONET/SDH networks. One important constraint is that the differential delay among the sub-paths should be limited (e.g. 25 ms, 45 ms, etc.). In this paper, we consider mechanisms for splitting a connection request while maintaining the differential delay constraint. In particular, we study two schemes: even splitting of connection bandwidth among the constituent sub-paths; and uneven splitting of connection bandwidth. The work also considers sub-paths that are not necessarily link-disjoint. The performance analysis shows that the uneven splitting mechanism can substantially improve performance in terms of blocking probability (and other metrics) compared to the even splitting mechanism.

In this paper, we have proposed an analytical model for optical networks with full wavelength conversion at the nodes. We have derived an analytical expression to compute the carried traffic on links of the network for fixed routing with uniform traffic distribution (UTD). The carried traffic on a link in the network is thinned proportionately based on the blocking probability of the other links on the route. The blocking probability of the network is estimated using Erlang fixed point approximation with the reduced load on the links. The channel utilisation at a particular load is derived using the blocking probability. Thus the analytical model gives an estimate of the blocking probability and the channel utilisation at any given load and is applicable to any network topology. We have computed the carried traffic for a few example networks, such as 14 node NSFNET, 20 node ARPANET and 20 node INDIANET and validated the analytical results with simulations. We show that the analytical method performs well in the desired range of blocking probabilities and it is computationally efficient.

In this paper we propose an approximation for individual overflow moments of a multiservice link with differing arrival rates, capacity requirements and mean holding times, where trunk reservation is used. The approximation is a generalization of Roberts' well-known approximation for individual blocking probabilities of a multiservice link to higher moments. It can be computed very efficiently. The quality of the approximation for the second moment (variance) is comparable to Roberts' approximation for the individual blocking probabilities. Thus the results provide an efficient algorithm for computing the two moment characterization of the individual overflow streams and hence can be used for the design and analysis of circuit switched alternate routing networks with trunk reservation links.

We consider a model for a single link in a circuit switched network. The link has C circuits, and the input consists of offered calls of two types, that we call primary and secondary traffic. Of the C links R are reserved for primary traffic. We assume that both traffic types arrive as Poisson arrival streams. Assuming that C is large and R=O(1), the arrival rate of secondary traffic is O(C) while that of primary traffic is smaller, of the order . The holding times of the secondary calls are assumed exponentially distributed with unit mean. Those of the primary calls are exponentially distributed with a large mean, that is . The loads for both traffic types are thus comparable (O(C)) and we assume that the system is “critically loaded,” i.e., the system's capacity is approximately equal to the total load. We analyze asymptotically the steady state probability that n2 (resp. n1) circuits are occupied by primary (resp. secondary) calls. In particular, we obtain two‐term asymptotic approximations to the blocking probabilities for both traffic types. This work complements part I, where we assumed that the secondary traffic had an arrival rate that was and a service rate that was . Thus in part I the R trunks were reserved for the “fast traffic,” whose arrival and service rates were O(C) and O(1).

The performance of non-hierarchical circuit switched networks at moderate load conditions is improved when alternate routes are made available. However, alternate routes introduce instability under heavy and overloaded conditions, and under these load conditions network performance is found to deteriorate. To alleviate this problem, a control mechanism that reserves a traction of the capacity of each link for direct routed calls is used. In this paper, a traffic management scheme is developed to enhance the performance of a mesh-connected, circuit-switched satellite communication network. The network load is measured and the network is continually adapted by reconfiguring the map to suit the current traffic conditions. The reconfiguration of the network is done by properly allocating the capacity of each link and placing an optimal reservation on each link. The optimization is done by using a neural network-based optimization technique called mean field annealing. The simulation results show that this method of traffic management performs better than pure dynamic routing with a fixed configuration. >

In circuit-switched networks it is well known that dynamic routing can provide significant throughput gain over fixed routing. Rerouting is the practice of routing calls currently on alternate paths to direct paths or other less congested alternate paths. Previous studies have shown that rerouting can not only increase the throughput of dynamic routing, but also maintain network stability without the need for trunk reservation. This article presents a taxonomy of rerouting in circuit-switched networks showing the various ways rerouting can be designed. In addition, a comparative study on a number of rerouting schemes are performed in a uniformly loaded, fully connected circuit-switched network.