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This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided.

This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.

A multi-server queueing system with synchronous differentiated working vacation policy, Bernoulli schedule vacation interruption, and customer impatience (balking and reneging) is studied. The system consists of c servers and a finite capacity N, where customers arrive according to a Poisson process and are served in the chronological order of their arrival. When the system becomes empty, servers wait for a random duration before entering a type-1 working vacation, during which service is provided at a reduced rate. If customers are present in the system at the moment of service achievement during this period, the vacation is interrupted. With a certain probability, servers return to the regular busy period; otherwise, they continue the working vacation. Upon completion of the working vacation, if the system is still empty, servers can take another working vacation of shorter duration, named type-2 working vacation; otherwise, they switch to the regular busy period. Customer impatience is considered during both the normal busy period and working vacations. A recursive analysis method is used to find the steady-state probabilities of the system. Then, some important performance measures are obtained. Furthermore, an optimal operational policy for the model is developed to minimize the total expected cost. The Grey Wolf Optimization (GWO) meta-heuristic approach is employed to determine the optimal service rates for both working vacations and normal busy periods. Finally, several numerical examples are provided to validate and support the theoretical findings. [ABSTRACT FROM AUTHOR]

In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.

We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server’s states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system.

The main objective of this paper is to investigate the problem of estimating the trend function St = S(xt) for process satisfying stochastic differential equations of the type dXt=S(Xt)dt+εdBtH,K, X0=x0, 0≤t≤T,{\rm{d}}{{\rm{X}}_{\rm{t}}} = {\rm{S}}\left( {{{\rm{X}}_{\rm{t}}}} \right){\rm{dt + }}\varepsilon {\rm{dB}}_{\rm{t}}^{{\rm{H,K}}},\,{{\rm{X}}_{\rm{0}}} = {{\rm{x}}_{\rm{0}}},\,0 \le {\rm{t}} \le {\rm{T,}}

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

The main objective of this paper is to non-parametrically estimate the quantiles of a conditional distribution in the censorship model when the sample is considered as an -mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we estimate the quantiles by inverting this estimated cond-cdf and state the asymptotic properties when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis.

This paper deals with the estimation of conditional distribution function based on the single-index model. The asymptotic normality of the conditional distribution estimator is established. Moreover, as an application, the asymptotic (1 − γ) confidence interval of the conditional distribution function is given for 0 < γ < 1.

We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server’s states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]