An Efficient Convolution Algorithm for the Non-Markovian Two-Node Cyclic Network

Consider a closed cyclic queueing model that consists of two nodes and a total of M customers. Each node buffer can accommodate all M customers. Node 1 has N ≤ M servers, each having an exponential service time with rate λ . The second node consists of a single server with a general service time distribution function B . . The well-known machine repair model with spares, where a set of identical machines, N , is served by a single repair person, is a key application of this model. This model has several other applications in performance evaluation, manufacturing, computer networks, and in reliability studies as it can be easily used to compute system availability. In this article, we give an efficient algorithm to derive an exact solution for the steady state system size probabilities. Our approach is based on developing an efficient polynomial convolution method to compute the transition probabilities of a birth process over node 2 service times and solving an imbedded Markov chain at node 2 service completion epochs. This is a significant improvement over the exponential algorithm given in an earlier paper. Numerical examples are given to demonstrate the performance of our method.

DISCRETE-TIME GIX/GEO/1/N QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTION

In this paper, we study a discrete-time finite buffer batch arrival queue with multiple geometric working vacations and vacation interruption: the server serves the customers at the lower rate rather than completely stopping during the vacation period and can come back to the normal working level once there are customers after a service completion during the vacation period, i.e., a vacation interruption happens. The service times during a service period, service times during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer's observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

A Novel Simplified Limit-1 Polling Communication System

proposed a Limit-1 polling system model with simplified service process (SL-1), which was analyzed by the theory of imbedded Markov chain and the method of multidimensional probability generating function. The related characteristic of system was obtained based on the analysis of polling mechanism. The contrast of numerical curve and simulation experiment between SL-1 service and Limit-1 service showed that the SL-1 service polling model performed better in queuing performance and stability.

Queue-Length Analysis of Continuous-Time Polling System with Vacations Using M-Gated Services

In this paper we consider the polling system with multiple vacations an bulk arrival using M-gated services in continuous time. By the imbedded Markov chain theory, the generating functions of queue length at the station is obtained. Then computational equations are explicitly determined for the mean queue length. Especially we can obtain some corresponding results under some especial cases. The results reveal that our system model can guarantee better QoS and system stability, and it has better efficiency than that of traditional gated service.

COUNTING OF OLIGOMERS IN SEQUENCES GENERATED BY MARKOV CHAINS FOR DNA MOTIF DISCOVERY

By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at .