تجزیه و تحلیل عملکرد از مسیریابی متناوب با رزرو صندوق عقب در شبکه های سوئیچ آداب و رسوم

The traditional approach to implementing call routing in PSTN networks uses trunk reservation to achieve high throughput by avoiding possible routing oscillations in dynamic alternate routing. The purpose of trunk reservation in PSTN networks that support only a single class of traffic, e.g. voice is to limit the use of alternate paths for call routing when the network is heavily loaded. In this paper, we model the system of dynamic alternate routing with trunk reservation for multirate switched networks where the Markov chain is not time reversible, and analyze it by using an iteration method. Then as the calculation to find the optimal reservation size is intractable, we slightly modify the conventional Kaufman's recursive method that has been applied for the reversible Markov chain system. The complexity of the modified approximation is the same as that of the Kaufman's method. For a network of which link capacity is 50 channels, the approximation shows quite similar results to the analysis. For a network of which link capacity is 750 channels, which state size is not workable, we compare our approximation with simulation results. If we count some computation errors caused by the reduced load effect in the approximation, we can conclude that our approximation is quite accurate. As alternate routing with trunk reservation is expected to run on the top of multirate switched networks, our proposed approach can be used to obtain the near optimal trunk reservation size in real time, which results in maximal throughput.

Dynamic routing of calls in circuit switched networks that support a single class of traffic, i.e., voice can improve throughput and robustness. Throughput is improved by establishing calls on alternate routes when the primary route is blocked. Robustness measured in terms of the network's ability to respond to unexpected network conditions, is improved by transferring calls to backup routes. Alternate routing with trunk reservation is the well-known dynamic routing scheme used to alleviate network congestion, and there is a large literature investigating the performance of variants of this scheme [1], [2], [3], [4], [5], [6], [7], [8] and [9]. However, diverse traffic patterns and statistical multiplexing of traffic in B-ISDN networks complicate the design of routing schemes. Users in B-ISDN networks require various levels of QoS, and they can be satisfied with appropriate bandwidth and buffer assignment [11], [12] and [13]. In this paper, we assume that a user's QoS can be mapped into bandwidth requirement only. If the network finds that a call's requested bandwidth size is smaller than the available bandwidth size, it accepts the call request. Otherwise it blocks the call. A lot of investigations have been done for single service loss networks where a call occupies exactly one circuit (or channel) in each link along its route [6]. Given the great gains in performance achieved by dynamic routing in single rate loss networks, it seems quite natural to apply similar routing techniques for B-ISDN networks. However, system modeling and analysis of dynamic routing in B-ISDN networks are not so simple as those in single rate networks. Especially modeling dynamic routing with trunk reservation requires much more work. This is basically due to inherent complexity in the modeled Markov system. In [9] and [10], single rate traffic for a couple of variants of dynamic routing was considered and relevant routing procedures were studied. These results are not simply applicable to multirate switched networks. In this paper we consider dynamic routing with trunk reservation in B-ISDN networks and develop the studies of [9] and [10]. In an attempt to analyze the given time irreversible system, we first formulate the system in an iterative form. As exact performance evaluation with the iterative method requires lots of computation, we try to obtain approximate performance by our modified Kaufman's recursive method. The reduction in computation time by this approximation is important for the trunk reservation routing algorithm to run on real networks because fast finding of the trunk reservation size is made possible, which allows the network to efficiently face network problems caused by abrupt network changes. Our proposed approximation gives accurate results to the problems of interest with acceptable complexity when compared with the exact analysis in a small size network. For a large size network where the analytical results from the iterative method are no longer available, we use simulation to evaluate the exactness of our approximation. This paper is organized as follows. We investigate the network model of the dynamic routing algorithm with trunk reservation in Section 2 for multirate switched networks. Section 3 deals with an approximate method to obtain its performance. The analysis and simulation results are compared with our approximation ones in Section 4 followed by the conclusion in Section 5.

In this paper we have studied the performance of alternate routing with trunk reservation in multiclass traffic supporting networks. As the modeled trunk reservation system shows a property of irreversible Markov chain, the conventional approaches could not be applied for analysis. Therefore we slightly modified the Kaufman's recursive formula to obtain the approximate steady state equilibrium probabilities. We compared the analysis with our approximation for a network with small link capacity of 50 channels and two traffic classes. The analytical solutions were very similar to the approximate ones. For a network with large link capacity of 750 channels and three traffic classes where the exact solutions are not available, we compared the simulation with our approximation. The simulation showed very close results to the approximation for all the loadings. Our approximation method has only C unknowns (g(t)) and they can be computed recursively. But the exact method has O(CK) unknowns (the probabilities of all states), and they can be solved by an inversion of the transition matrix whose size is O(CK) by O(CK). Since the complexity of our approximation method is so low, the network can determine optimal trunk reservation size in real time under time varying traffic loading. In conclusion, the purpose of this paper was to (i) model the trunk reservation based routing scheme for multiclass call environments, (ii) propose an approximate model to solve this model with low complexity that can be applicable for a large size network, and (iii) show the validity of our approximate method by comparing its results with the exact calculation results for a small size network, and with the simulation results for a large size network. As alternate routing with trunk reservation is widely accepted in current single rate switched networks because of its good performance, it may be used for B-ISDN routing in the long run. In this case our modeling and approximation can be used to decide the optimal trunk reservation size in a very efficient manner. Also if the trunk reservation based routing scheme considers long lived calls studied in Ref. [15], its effectiveness will be much increased.