A Queueing Model of General Servers in Tandem with Finite Buffer Capacities
نویسنده
چکیده
We consider a queueing model with finite capacities. External arrivals follow a Coxian distribution. Due to the limitation of the capacity, arrivals may be lost if the buffer is full. Our goal is to study the probability of blocking. In order to obtain the steady-state probability distribution of this model, we construct an embedded Markov chain at the departure points. The solution is solved analytically and its analysis is extended to semi-Markovian representation of performance measures in queueing networks. KeywordsQueueing Networks, Probability Distribution, Embedded Markov Chain. * Corresponding author’s email: [email protected]
منابع مشابه
On Two-Echelon Multi-Server Queue with Balking and Limited Intermediate Buffer
In this paper we study two echelon multi-server tandom queueing systems where customers arrive according to a poisson process with two different rates. The service rates at both echelons are independent of each other. The service times of customers is assumed to be completed in two stages. The service times at each stage are exponentially distributed. At the first stage, the customers may balk ...
متن کاملTandem queueing system with impatient customers as a model of call center with Interactive Voice Response
A tandem queueing system with a Markovian Arrival Process (MAP) useful in modeling a call center with Interactive Voice Response (IVR) is investigated. The first stage has a finite number of servers without buffer while the second stage of the tandem has a finite buffer and a finite number of servers. The service time at the first (second) stage has an exponential (phase type) distribution. A s...
متن کاملThroughput maximization for two station tandem systems: a proof of the Andradóttir-Ayhan conjecture
We study a tandem queueing network with two stations, M heterogeneous flexible servers, and a finite intermediate buffer. The objective is to dynamically assign the servers to the stations in order to maximize the throughput of the system. The form of the optimal policy for M ≤ 3 was derived in two previous papers. In one of those papers, Andradóttir and Ayhan (Operations Research, Vol. 53, pp....
متن کاملAnalysis and Approximation of Dual Tandem Queues with Finite Buffer Capacity
Tandem queues with finite buffer capacity commonly exist in practical applications. By viewing a tandem queue as an integrated system, an innovative approach has been developed to analyze its performance through the insight from Friedman's reduction method. Fundamental properties of tandem queues with finite buffer capacity are examined. We show that in general system service rate of a dual tan...
متن کاملM M m K Queue With Additional Servers and Discouragement (RESEARCH NOTE)
Waiting in long queue is undesirable due to which in some practical situations customers become impatient and leave the system. In such cases providing additional servers can reduce long queue. This investigation deals with multi-server queueing system with additional servers and discouragement. The customers arrive in poisson fashion and are served exponentially by a pool of permanent and addi...
متن کامل