Cellular network design must incorporate disaster response and repair scenarios. Requirements for high reliability and low latency often fail to incorporate network survivability for mission critical services. This paper defines a practical modeling approach using a Markov chain Matrix Exponential (ME) model. Transient and the steady state representations of system repair models, namely, fast and slow (i.e., crew-based) repairs for networks consisting of a multiple repair crews have been analyzed. Failures are exponentially modeled as per common practice, but ME distributions describe the more complex recovery processes. The model used in this paper is evaluated for varying number of repair crews, base stations, repair models and squared coefficient of variation values. This model is scalable for larger networks, calculates the restoration and network availability times, consists of asymptotic approximations to estimate network availability and determines the optimal number repair crews required. This ME model shows how survivable networks can be designed based on controlling numbers of crews, times taken for individual repair stages in the repair process, and the balance between fast and slow repairs.

In this paper, we attempt to improve the performance in congested parts (CP) of an asymmetric network using network controls and routing mechanisms. Typically, an asymmetric network is characterized by non-uniform link capacities or uneven traffic load or both. In such a network, certain service classes can experience poor performance in parts of the network, even when the average performance is very close to the expected performance level. We studied a network derived from an actual service provider network with asymmetric concentration of traffic. We have developed two metrics in order to capture the congested part behavior in a network. In order to understand the generality of our conclusions, we used three variations of our network and show that controls like service class based multi-link dynamic capacity reservation (SMDCR) with a properly chosen reservation factor, significantly reduce variability in the performance over all parts of the network.

In this paper, we attempt to understand the benefits of MPLS traffic engineering through a case study. Specifically, we do a comparative study of MPLS traffic engineering in the presence of dynamic constraint-based routing compared to destination-based routing. For this case study, we use a model derived from an actual service provider network. Different control schemes that can be deployable for MPLS traffic engineering are also considered. This case study shows that services can indeed obtain benefits from constraint-based routing and traffic engineering controls.

In this paper we present an analytical model for micro- and pico-cell wireless networks for any arbitrary topology in a high mobility feedforward environment. We introduce an approximation technique which uses a single-cell decomposition analysis which incorporates moment matching of handoff processes into the cell. The approximation technique can provide close approximations for non-Poisson arrival traffic and it is easily parallelized. Performance measures such as new calls blocked, handoff calls lost, and forced termination are derived for any general independent call arrival distribution in a heterogeneous traffic environment. We produce some numerical examples for some simple topologies with varying mobility for several call arrival distributions and compare our results to those from simulation studies.

In this paper we present an analytical model for microcellular and picocellular wireless networks for any arbitrary topology in a high-mobility environment. We introduce an approximation technique which uses a single-cell decomposition analysis which incorporates moment matching of hand-off processes into the cell. The approximation technique is novel in that it can provide close approximations for non-Poisson arrival traffic and it is easily parallelized. Performance measures such as new calls blocked and hand-off calls lost are presented for any general call arrival distribution in a non-homogeneous traffic environment. We produce some numerical examples for some simple topologies with varying mobility for several call arrival distributions and compare our results to those from simulation studies.

Presents a unified model to compute various performance measures when Poissonian and non-Poissonian (renewal) multi-slot traffic streams are offered to a digital link in a (double) loss system. the authors represent the non-Poissonian arrival process by a matrix-exponential distribution, requiring only that the inter-arrival distribution has a rational Laplace transform. Several distributions are considered as the non-Poissonian traffic. The resulting model uses matrix algebraic techniques only, thus not requiring any complex and/or tedious transform techniques. The authors also incorporate various control policies in their modeling framework using acceptance functions. Through computational studies, they conclude that the second and the third moments of the non-Poissonian traffic have significant impact on various performance measures.>

The linear algebraic approach to queuing theory is applied to analyze the performance of a typical single-bus multiprocessor system. This system can be modeled as an M/G/1/N queuing system with load-dependent arrivals. The method presented requires only that the nonexponential service time distribution for the system be a matrix-exponential, that is, one with a rational Laplace transform. Using linear algebraic techniques, expressions are obtained for the performance characteristics of interest, such as the processing power for the multiprocessor system. The algorithm does not rely on root finding and can be implemented using symbolic programming techniques. The explicit closed-form expression for the processing power is presented for some special cases.>

A divide-and-conquer approach for the presumed minimal solution to the Reve's puzzle, the Tower of Hanoi with four pegs, leads to a simple structure of the solution. In particular, it allows an easy, iterative algorithm – for the three-peg problem – to be extended to four pegs.

An explicit steady-state solution is given for any queuing loop made up of two general servers, whose distribution functions have rational Laplace transforms. The solution is in matrix geometric form over a vector space that is itself a direct or Kronecker product of the internal state spaces of the two servers. The algebraic properties of relevant entities in this space are given in an appendix. The closed-form solution yields simple recursive relations that in turn lead to an efficient algorithm for calculating various performance measures such as queue length and throughput. A computational-complexity analysis shows that the algorithm requires at least an order of magnitude less computational effort than any previously reported algorithm.