The main aim of this paper is to examine issues relating to the performance of various Telecommunication networks, and applied queuing theory for better design and improved efficiency. Firstly, giving an analytical study of queues deals with quantifying the phenomenon of waiting lines using representative measures of performances, such as average queue length (on average number of customers in ...

Abstract: The present investigation deals with M/G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair. The server renders first essential phase of service (FES) to all the arriving customers whereas second optional phase services (SOS) are provided after FES to only those customers who opt fo...

Abstract: In this paper, we study a discrete time queueing system with multiple types of customers and a last-come-first-served general preemptive resume (LCFS-GPR) service discipline (MMAP[K]/PH[K]/1/LCFS-GPR). When the waiting space is infinite, matrix analytic methods are used to find a system stability condition, to derive the distributions of the busy periods and sojourn times, and to obta...

In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential service, he can also facilitate the additional phase of optional service (OS) in batches of fixed size b(≥ 1), in case when the customers request for it. The serv...

In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and low priority customers. For this situation the following service disciplines are considered: gated, globally gated, and exhaustive. We study the cycle time dis...

We consider a bulk service G I / M / l queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, I\) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We des...

In this note, we consider a single server queue with gated processor-sharing discipline. Customers arrive according to a Poisson process with rate A and service times are independent and identically distributed (i.i.d.) as an arbitrary random variable S with distribution function H(t) and LST H(s). In the gated processor-sharing discipline, when an arriving customer finds the queue empty, he is...

In many service industries, companies compete with each other on the basis of the waiting time their customers experience, along with the price they charge for their service. A firm’s waiting-time standard may either be defined in terms of the expected value or a given, for example 95%, percentile of the steady state waiting-time distribution. We investigate how a service industry’s competitive...

Customers move through a series of M service stations. Each customer, independent of all others, requires service from only one of the stations, for a duration of 1 time unit, this being station i with probabilityp1. The customer has zero service at all the other stations, but there is no overtaking between the customers, and so queueing occurs. In the case where there is unlimited waiting room...