The behavioral equivalence that is typically used to relate Markovian process terms and to reduce their underlying state spaces is Markovian bisimilarity. One of the reasons is that Markovian bisimilarity is consistent with ordinary lumping. The latter is an aggregation for Markov chains that is exact, hence it guarantees the preservation of the performance characteristics across Markovian bisi...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...

Keywords: Queueing Tandem queueing system Marked Markovian arrival process Phase-type distribution Laplace–Stieltjes transform a b s t r a c t A tandem queueing system with infinite and finite intermediate buffers, heterogeneous customers and generalized phase-type service time distribution at the second stage is investigated. The first stage of the tandem has a finite number of servers without...

We consider the estimation of hidden Markovian process by using information geometry with respect to transition matrices. We consider the case when we use only the histogram of k-memory data. Firstly, we focus on a partial observation model with Markovian process and we show that the asymptotic estimation error of this model is given as the inverse of projective Fisher information of transition...

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 ...

In this paper a two-state Markovian maintenance process where the true state is unknown will be considered. The operating cost per period is a continuous random variable which depends on the state of the process. If investigation cost is incurred at the beginning of any period, the system wit I be returned to the "in-control" state instantaneously. This problem is solved using the average crite...