We study the departure process of a single server queue with Markovian arrival input and Markov renewal service time. We derive the joint transform of departure time and the number of departures and, based on this transform, we establish several expressions for burstiness (variance) and correlation (covariance sequence) of the departure process. These expressions reveal that burstiness and corr...

The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discrete-time synchronous update rule. We give theoretical support that the overlap of systems' states between the current and a previous time develops in time according to a Markovian stochastic process in large networks. This Markovian process predicts how often...

EMPA enhances the expressiveness of classical process algebras by integrating functional and performance descriptions of concurrent systems. This is achieved by ooering, besides passive actions (useful for pure nondeterminism), actions whose duration is exponentially distributed as well as immediate actions (useful for performance abstraction), parametrized by priority levels (hence prioritized...

Abstract Here a two-state batch arrivals and batch service Markovian queue with server vacation model has been taken into consideration for its mathematical modelling and performance analysis under transient state. The present Markovian queueing model considers a single server with multiple vacations and both arrivals and services in batches of variable size. Arriving customers are processed by...

Characterization protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable impressive feats. This trajectory is expected to continue building next generation devices—ones that can surpass classical for particular tasks—but progress characterization must keep up with complexities intricate device noise. A missing piece zoo procedu...

Recently the so-called Prabhakar generalization of fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal waiting times between events are IID continuous random variables. present paper we analyze discrete-time counterparts: Renewal processes with integer interarrival which converge in well-scaled continuous-time limits Pr...

This paper studies two stochastic batch Markovian arrival and batch Markovian service single server queue BMAP/BMSP/1 queue Models (A) and (B) with randomly varying k* distinct environments. The arrival process of the queue has matrix representation {Dm i : 0 ≤ m ≤ M} of order ki describing the BMAP and the service process has matrix representation {Sn i : 0 ≤ n ≤ N} of order k′i describing the...

We derive the performance measures for non-priority customers in a priority single-server queue with two types of Markovian arrival processes (MAPs). One type of customers has preemptive resume (or repeat) priority over the other. We regard the model with two types of MAP arrivals as an MAP/SM/l queue with only non-priority customers arrivals, semi-Markovian service times and some server vacati...

The strong L2-approximation of occupation time functionals is studied with respect to discrete observations a d-dimensional càdlàg process. Upper bounds on the error are obtained under weak assumptions, generalizing previous results in literature considerably. approach relies regularity for marginals process and applies also non-Markovian processes, such as fractional Brownian motion. used appr...