Abstract
In this paper, we analyze a multi-server queueing system with heterogeneous customers that arrive according to a marked Markovian arrival process. Customers of two types differ in priorities and parameters of phase type distribution of their service time. The queue under consideration can be used to model the processes of information transmission in telecommunication networks in which often the flow of information is the superposition of several types of flows with correlation of inter-arrival times within each flow and cross-correlation. We define the process of information transmission as the multi-dimensional Markov chain, derive the generator of this chain and compute its stationary distribution. Expressions for computation of various performance measures of the system, including the probabilities of loss of customers of different types, are presented. Output flow from the system is characterized. The presented numerical results confirm the high importance of account of correlation in the arrival process. The values of important performance measures for the systems with the correlated arrival process are essentially different from the corresponding values for the systems with the stationary Poisson arrival process. Measurements in many real world systems show poor approximation of real flows by such an arrival process. However, this process is still popular among the telecommunication engineers due to the evident existing gap between the needs of adequately modeling the real life systems and the current state of the theory of algorithmic methods of queueing theory.
Highlights
One of the essential sections of the queuing theory is the theory of priority systems.In such systems, customers of different classes are assigned different categories of importance and service is carried out in accordance with a priority scheme
Priority queueing models arise in many real world applications
We present the results of numerical experiments that allow us to estimate the effect of the input rate λ and correlation in the marked Markovian arrival process (MMAP) on the system performance measures
Summary
One of the essential sections of the queuing theory is the theory of priority systems. Level Agreement (SLA), whereby certain customers have chosen to pay more so as to get high-priority access to some high-demand resource Another set of potential applications of the priority queueing model like considered in our paper is described in [3] as applications in customer service centers, see [4], airport security checkpoints [5], hospital emergency rooms [6], cloud computing systems [7] or processor management in certain computer operating systems [8]. We consider a priority MMAP/PH1,2 /N/N queueing system with two types of customers As it is pointed out above, analysis of such multi-server systems is very important for practice, these systems did not get a proper portion of attention of queueing theorists.
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