Service Oriented Computing (SOC) is a design paradigm that has evolved from earlier paradigms including object-orientation and component-based software engineering. Important features of services are compositionality, context-independence, encapsulation and re-usability. To support the formal design and analysis of SOC applications recently a number of Service Oriented Calculi have been propose...

Several Markovian process calculi have been proposed in the literature, which differ from each other for various aspects. With regard to the action representation, we distinguish between integrated-time Markovian process calculi, in which every action has an exponentially distributed duration associated with it, and orthogonal-time Markovian process calculi, in which action execution is separat...

We derive the two-dimensional transforms of the transient workload and queue-length distributions in the single-server queue with general service times and a batch Markovian arrival process (BMAP). This arrival process includes the familiar phase-type renewal process and the Markov modulated Poisson process as special cases, and allows correlated interarrival times and batch sizes. Numerical re...

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...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian SIS process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1/ ln(λ1 + 1), whe...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infect...

We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on ...

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. Scaling the arrival rates λi by a factor N , tail probabilities are examined when letting N tend to∞; non-standard large deviations results are obtained. An importance-sampling based estimation algori...