This paper introduces a numerical solution method for a class of discrete-time polling systems by relying on the power method, Kronecker matrix representations and the shuffle algorithm. The class of polling models considered consists of several infinite pseudo queues, deterministic service times, Bernoulli service and Markovian routing and includes exhaustive, 1-limited and k-limited service a...

banking and financial services are important parts of the service industry. quality of service in the banking industry has a close relationship with customer satisfaction service system. banks could create competitive advantage by increasing customer satisfaction and reduce costs in today's competitive environment. this paper presents a decision-making model to obtain optimum tasks assigne...

This paper proposes a unified matrix-analytic approach to characterize the output processes of general discrete-time lossless/lossy queueing systems in which time is synchronized/slotted into fixed length intervals called slots. The arrival process can be continuousor discrete-time Markovian processes. It can be either renewal or non-renewal. The service of a customer commences at the beginning...

The present paper contains a specification of the EM algorithm in order to fit an empirical counting process, observed at discrete times, to a Markovian arrival process. The given data are the numbers of observed events in disjoint time intervals. The underlying phase process is not observable. An exact numerical procedure to compute the E and M steps is given.

Service-oriented computing is dynamic. There may be many possible service instances available for binding, leading to uncertainty about where service requests will execute. We present a novel Markovian process calculus which allows the formal expression of uncertainty about binding as found in service-oriented computing. We show how to compute meaningful quantitative information about the quali...

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the los...

The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order β ∈ (0, 1) . The fundamental solution for the Cauchy problem is interpreted as a probability density of a selfsimilar non-Markovian stochastic process related to a phenomenon of subdiffusion (the variance grows in time sub-lin...

This paper presents an algorithmic procedure to calculate the queue length and delay distribution of customers in a discrete time D-MAP/PH/1 queue, where the service time distribution of a customer depends on the inter-arrival time between himself and his predecessor. Setting up a Markov chain that keeps track of the contents of such a queue will result in a state space explosion as the inter-a...

We assess the performance of a partially shared bottleneck buffer for scalable video. The arrival process of the video packets is modelled by means of a two-class discrete batch Markovian arrival process. Using a matrix-analytic approach, we retrieve various performance measures. We illustrate our approach by means of a numerical example.