In this paper we propose a novel MATLAB tool, called Q-MAM, to compute queue length, waiting time and sojourn time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1and GI/M/1-type, quasi-birth-death and non-skip-free Markov chains (implemented by the SMCSolver tool), as well as Markov ...

Abstract Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBMAP ) has been widely used to model the source behavior of data traffic, while phase-type (PH) distribution has been extensively applied to model the serv...

We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1-limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routi...

In this paper, we investigate the delay-dependent robust stability of fuzzy Cohen-Grossberg neural networks with Markovian jumping parameter and mixed time varying delays by delay decomposition method. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing discrete delay interval into multiple subinterval, and choosing proper functionals with different weighting matr...

Discrete-time queueing models find a large number of applications as they are used in modeling systems arising digital platforms like telecommunication and computer networks. In this paper, we analyze an infinite-buffer model with discrete Markovian arrival process. The units on served batches by single server according to the general bulk-service rule, service time follows distribution rate de...

Abstract. Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of cust...

Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary ...

Abstract This paper considers a FIFO single-server queue with service interruptions and multiple batch Markovian arrival streams. The server state (on and off), the type of arriving customers and their batch size are assumed to be governed by a continuous-time Markov chain with finite states. To put it more concretely, the marginal process of the server state is a phase-type alternating Markov ...

A state estimator design is described for discrete time systems having observably intermittent measurements. A stationary Markov process is used to model probabilistic measurement losses. The stationarity of the Markov process suggests an analagous stationary estimator design related to the Markov states. A precomputable time-varying state estimator is proposed as an alternative to Kalman’s opt...

In a recent work we introduced semi-Markovian discrete-time generalization of the telegraph process. We referred to this random walk as ‘squirrel walk’ (SRW). The SRW is on one-dimensional infinite lattice where step direction reversed at arrival times renewal process and remains unchanged uneventful time instants. first recall general notions SRW. main subject paper study switches Sibuya (GSP)...