The mathematical model of the retrial queuing system \(M^{[n]}/M/1\) with feedback and batch Poisson arrival is constructed. Customers arrive in groups. If server free, one arriving customers starts his service, rest join orbit. service times are exponentially distributed. customer whose completed leaves system, or reservice, goes to method asymptotic diffusion analysis proposed for finding pro...

Parallel zu diesen Entwicklungen stiegen die Anforderungen an die Methoden zur Leistungsanalyse derartiger Systeme. Die Warteschlangentheorie stellt klassische Modelle zur Analyse von Kommunikationsnetzen bereit. Ein Bereich in der modernen Warteschlangentheorie sind die Matrix analytischen Methoden. Hier konzentriert sich die Forschung auf den Batch Markovian Arrival Process (BMAP), welcher äq...

Control of batch processors is one of the most important issues in semiconductor manufacturing. Ineffective dispatching policies may cause an increase in overall cycle time. This paper presents a real-time scheduling heuristic for a production unit consisting of a serial processor feeding a batch processor. In this multiple product batching problem, our objective is to reduce the average waitin...

We treat a single–server vacation queue with queue–length dependent vacation schedules. This subsumes the single–server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch–Markovian arrival pro...

We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/I model is a relatively simple matrix generalization of the M/G/l queue. Stationary and transient distributions for t...

In this paper, we considered a batch arrival feedback retrial queue with two phase of service under Bernoulli vacation schedule and orbit search. At the arrival epoch of a batch, if the server is busy, under repair or on vacation then the whole batch joins the orbit. Where as if the server is free, then one of the arriving customers starts his service immediately and the rest join the orbit. At...

We consider the problem of dynamic allocation of a single server with batch processing capability to a set of parallel queues+ Jobs from different classes cannot be processed together in the same batch+ The arrival processes are mutually independent Poisson flows with equal rates+ Batches have independent and identically distributed exponentially distributed service times, independent of the ba...

In this paper we present a UMTS traffic model to evaluate the Measurement Based Admission Control (MBAC) algorithms in a simulator environment. The traffic model describes the traffic aggregation at the Base Station (BS) and Radio Network Controller (RNC) with a Markov Modulated Arrival Process (MMAP). In the model we describe the batch and packet sizes in the Radio Access Network (RAN). Furthe...