A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations

Performance and economic evaluation of differentiated multiple vacation queueing system with feedback and balked customers

The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented

Conditional full support for Fractional Brownian Motion

In this paper we establish conditions that imply the conditional full support (CFS) property, introduced by Guasoni et al. (2008), for the processes St where BH is a Fractional Brownian motion, R is a continuous process, and the processes R and φ are either progressive or independent of BH: Moreover we build the absence of arbitrage opportunities without calculating the risk-neutral probability

Stability Condition of a Retrial Queueing System with Abandoned and Feedback Customers

This paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system after a random time. After the customer is served completely, the customer will decide either to join the retrial group again for another service or leave the system forever with some probability

On a Multiserver Queueing System with Customers’ Impatience Until the End of Service Under Single and Multiple Vacation Policies

This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented

Nonparametric Estimation of Trend Function for Stochastic Differential Equations Driven by a Weighted Fractional Brownian Motion

In this paper, we consider the problem of nonparametric estimation of trend function for stochastic differential equations driven by a weighted fractional Brownian motion (weighted-fBm). Under some general conditions, the consistent uniform, the rate of convergence as well as the asymptotic normality of our estimator are established. In addition, a numerical example is provided to illustrate the validity of the considered estimator