We consider a state-dependent Mn/Gn/1 queueing system with both finite and infinite buffer sizes. We allow the arrival rate of customers to depend on the number of people in the system. Service times are also statedependent and service rates can be modified at both arrivals and departures of customers. We show that the steady-state solution of this system at arbitrary times can be derived using...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

The notion of equivalence that is typically used to relate Markovian process terms and to reduce their underlying state spaces is Markovian bisimilarity. The reason is that, besides being a congruence, Markovian bisimilarity is consistent with ordinary lumping, an exact aggregation for Markov chains. In this paper we show that two non-bisimulation-based Markovian behavioral equivalences – Marko...

Customer retention is the key issue in the organizations facing the problem of customer impatience. Firms are employing a number o f customer retention strategies to sustain their businesses. An impatient customer (due to reneging) may be convinced to stay in service system for his service by utilizing certain convincing mechanisms. Such customers are termed as retained customers. Queuing with ...

Queuing models provide an attractive and highly-efficient alternative to simulation for quantifying traffic flow efficiency. Stationary Markovian queuing models in which both inter-arrival times and service times are exponentially distributed have been studied by the National Airspace System (NAS). However, stationary queues cannot account for peaks and valleys in demand that are commonly obser...

To describe the congestion in large-scale service systems, we introduce and analyze a non-Markovian open network of many-server fluid queues with customer abandonment, proportional routing and time-varying model elements. A proportion of the fluid completing service at each queue is routed immediately to each other queue, while the fluid not routed to other queues leaves the network. The fluid ...

we compare two approaches for a markovian model in flexible manufacturing systems (fmss) using monte carlo simulation. the model which is a development of fazlollahtabar and saidi-mehrabad (2013), considers two features of automated flexible manufacturing systems equipped with automated guided vehicle (agv) namely, the reliability of machines and the reliability of agvs in a multiple agv jobsho...

Motivated by large-scale service systems with network structure and non-exponential customer abandonment, in a previous paper we introduced a non-Markovian time-varying open network of many-server fluid queues with customer abandonment from each queue and timevarying proportional routing among the queues, and showed how performance functions can be determined. The deterministic fluid model serv...

This paper provides an analytical model for the performance evaluation of a two class DiffServ link. It is applicable for the performance analysis of Data traffic in the presence of higher priority Constant Bit Rate (CBR) encoded Voice and Video traffic. The DiffServ link is modeled as a single server queue in a Markovian environment. The queueing performance of data packets is evaluated by mat...

This paper studies an infinite-server queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates λi by a factor N and the transition rates νij of the background process as ...