Abstract
A multiserver queueing system, the dynamics of which depends on the state of some external continuous-time Markov chain (random environment, RE), is considered. Change of the state of the RE may cause variation of the parameters of the arrival process, the service process, the number of available servers, and the available buffer capacity, as well as the behavior of customers. Evolution of the system states is described by the multidimensional continuous-time Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for the key performance measures are given. Numerical results illustrating the behavior of the system and showing possibility of formulation and solution of optimization problems are provided. The importance of the account of correlation in the arrival processes is numerically illustrated.
Highlights
Queueing theory is widely used for decision making about the resources needed to provide service in a variety of real life systems including contact centers, intelligent transportation systems, telecommunication networks, manufacturing and administrative systems, and banking
Numerical results illustrating the behavior of the system and showing possibility of formulation and solution of optimization problems are provided
In contrast to the classical queueing models, where the parameters and the distributions characterizing arrival, service, and other processes describing dynamics of the system are assumed to be fixed in advance, queues operating in the random environment (RE) presuppose that some or all parameters may dynamically vary due to influence of some external medium called RE
Summary
Queueing theory is widely used for decision making about the resources needed to provide service in a variety of real life systems including contact centers, intelligent transportation systems, telecommunication networks, manufacturing and administrative systems, and banking. The queueing systems that incorporate both normal queues and retrial orbits are called hybrid retrial queues The importance of their investigation stems from the fact that many modern technologies of customers random access assume the existence of some places where the customers, who did not succeed to get access upon arrival, may be temporarily kept (in registers for handover customers in cells of mobile communication networks, in IVR (Interactive Voice Response) machines in call centers, etc.). Such hybrid systems were considered, for example, in [16, 17].
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