This paper proposes aggregation-based, three-stage algorithms to overcome the numerical problems encountered in computing stationary distributions and mean first passage times for multi-modal birth-death processes of large state space sizes. The considered birth-death processes which are defined by Chemical Master Equations are used in modeling stochastic behavior of gene regulatory networks. Computing stationary probabilities for a multi-modal distribution from Chemical Master Equations is subject to have numerical problems due to the probability values running out of the representation range of the standard programming languages with the increasing size of the state space. The aggregation is shown to provide a solution to this problem by analyzing first reduced size subsystems in isolation and then considering the transitions between these subsystems. The proposed algorithms are applied to study the bimodal behavior of the lac operon of E. coli described with a one-dimensional birth-death model. Thus, the determination of the entire parameter range of bimodality for the stochastic model of lac operon is achieved.

The article discusses the use of the diffusion approximation in transient analysis of queueing models applied to investigate some aspects of Internet transmissions. In classical queuing theory, the analysis of transient states is complex and practically does not go far beyond M/M/1 queue and its modifications. However, the time dependent flows in computer networks and especially in Internet focus our interest on transient-state analysis, which is necessary to investigate the dynamics of TCP flows cooperating with active queue management or to see the changes of priority queues which assure the differentiated QoS. With the use of G/G/1/N and G/G/1/N/PRIOR models, we present the potentials of the diffusion approximation and compare it with alternative methods: Markovian queues solved numerically, fluid-flow approximation and simulation. We mention briefly an original software we dispose to use these methods.

A method for modeling a spatial priority mechanism called the push-out buffer management policy is proposed. It is a known mechanism which takes into account two kinds of cells: vital and ordinary ones. It also ensures a high degree of flexibility for asynchronous transfer mode (ATM) services. The use of the diffusion approximation allows modeling general interarrival and service time distributions. The developed transient solution helps describe the burstiness of the flow of cells arriving at a node. The model may be useful for dimensioning network buffers within ATM networks.>

The performance of parallel computing in a network of Apollo workstations where the processes use the remote procedure call (RPC) mechanism for communication is addressed. The speedup in such systems cannot be accurately estimated without taking into account the relatively large communication overheads. Moreover, it decreases by increasing parallelism when the latter exceeds some certain limit. To estimate the speedup and determine the optimum degree of parallelism, the author characterizes the parallelization and the communication overheads in the system considered. Then, parallel applications are modeled and their execution times are expressed for the general case of nonidentical tasks and workstations. The general case study allows the structural constraints of the applications to be taken into account by permitting their partitioning into heterogeneous tasks. A simple expression of the optimum degree of parallelism is obtained for identical tasks where the inherent constraints are neglected. The fact that the theoretical maximum speedup is bounded by half of the optimum degree of parallelism shows the importance of this measure.>

A Boltzmann machine architecture to solve the problems of maximum independent set, set partitioning, clique, minimum vertex cover, minimum set cover, and maximum set packing is described. The authors evaluate the maximum and the average error of the method where the error is defined as the ratio of the cardinality of the obtained solution for an instance with respect to the optimal one. The results are compared with those obtained from the implementation of the heuristic described by D.S. Johnson (1974). The model treats the general case of all these problems that is the case when costs are associated with the data (vertices or subsets). The unweighted case becomes a particular case in this approach. It is shown that the model finds optimal solutions for a large percentage of the treated instances and provides a good performance ratio for the rest.>