An Erlang Loss Queue with Time-Phased Batch Arrivals as a Model for Traffic Control in Communication Networks
نویسندگان
چکیده
A multiserver queueing model that does not have a buffer but has batch arrival of customers is considered. In contrast to the standard batch arrival, in which the entire batch arrives at the system during a single epoch, we assume that the customers of a batch flow arrive individually in exponentially distributed times. The service time is exponentially distributed. Flows arrive according to a stationary Poisson arrival process. The flow size distribution is geometric. The number of flows that can be simultaneously admitted to the system is under control. The loss of any customer from an admitted flow, with a fixed probability, implies termination of the flow arrival. Analysis of the sojourn time and loss probability of an arbitrary flow is performed.
منابع مشابه
The Dynamic Analysis and Design of A Communication link with Stationary and Nonstationary Arrivals
Most research in queueing theory is typically based on the steady-state analysis. In today’s dynamically changing traffic environment, the steady-state analysis may not provide enough information to operators regarding Quality of Service (QoS) requirements and dynamic design. In addition, the steady state analysis is not practical for nonstationary arrivals. In this paper, we consider the time-...
متن کاملProduct-forms in batch networks: Approximation and asymptotics
It is shown that a Markovian queue, with bulk arrivals and departures having any probability mass functions for their batch sizes, has geometrically distributed queue length at equilibrium (when this exists) provided there is an additional special bulk arrival stream, with particular rate and batch size distribution, when the server is idle. It is shown that the time-averaged input rate of the ...
متن کاملA Unified Method to Analyze Overtake Free Queueing Systems
In this paper we demonstrate that the distributional laws that relate the number of customers in the system (queue), L(Q) and the time a customer spends in the system (queue), S(W) under the first-in-first-out (FIFO) discipline are special cases of the H = AG law and lead to a complete solution for the distributions of L, Q, S, W for queueing systems which satisfy distributional aws for both L ...
متن کاملTwo Approaches to Simulating Loss Networks
For multiservice loss networks the calculation of the normalization constant is computationally impossible for realistic sized problems. This paper deals with two methods for simulating the loss probabilities in multiservice loss networks. The regenerative method is based on the regenerative nature of the process and the simulation is carried out by simulating the DTMC of the process. The secon...
متن کاملPerformance Distributions of Queues with Batch Renewal Arrivals: GI/M/1/N and GI/Geo/1/N
It has been proven that the batch renewal process is the least biased choice of traffic process given the infinite sets of measures of the traffic correlation, (i.e. indices of dispersion, covariances or correlation functions) in the discrete time domain. The same conclusion is expected to hold in the continuous time domain. That motivates the study and comparison of similar queues, fed by batc...
متن کامل