the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We consider an M [x] /G/1 queue with two types of service subject to random breakdowns having multiple server vacation, where the customers arrive to the system in batches of variable size. We assume that a single server p...

Consider a single server retrial queueing system with preemptive priority service and single working vacation in which two types of customers arrive in a Poisson process with arrival rates λ1 for low and λ2 for high priority customers. We assume that regular service times follow an exponential distribution with parameters μ1 and μ2 correspondingly. The retrial is introduced for low priority cus...

In this contribution we investigate discrete-time queueing systems with vacations. A framework is constructed that allows for studying numerous different vacation systems, including a.o. classical vacation systems like the exhaustive and limited vacation systems as well as queueing systems with service interruptions. Using a probability generating functions approach, we obtain steady-state perf...

This paper refers to some closed two-stage queueing systems with state-dcpendent vacation policy. By means of the markovian rcnewal process and the stochastic decomposition formulas of the quantities in equilibrium for M/Gjl vacation models, we derive both stationary distributions of the queue length and the cyclic time for the closed state-dependcnt vacation model. We try to so!\'e the problem...

Consider an M/M/1 queueing system with server vacations where the server is turned oo as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding co...

The present investigation deals with performance analysis of single server preemptive priority retrial queue with immediate Bernoulli feedback. There are two types of customers are considered, which are priority customers and ordinary customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. After complet...

This paper is devoted to the study of an M/G/1 queue with a particular vacation discipline. The server is due to take a vacation as soon as it has served exactly N customers since the end of the previous vacation. N may be either a constant or a random variable. If the system becomes empty before the server has served N customers, then it stays idle until the next customer arrival. Such a vacat...

This paper treats two-threshold policies for an M/G/1 queue with two types of generally distributed random vacations: type 1 (long) and type 2 (short) vacations. Upon returning from a vacation, the server observes the queue length. If this is less than the lower threshold, the server takes a type 1 vacation; if it is between the two thresholds, the server takes a type 2 vacation; and if it is a...

why version: answers the question “Why are you going on vacation?” I feel like a long vacation, somewhere far away. I love to travel. Mexico has places where I can relax and also see some amazing natural landscapes. That’s why I choose Mexico as the destination. There are great beaches and many important cultural sites Clark, Semin / Conversational Relevance 165

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Ber...