Dear Colleagues,

Queueing system models have various different applications in many areas. The headway made in engineering systems, the economy, and computer science in the past few years has caused these systems to often be used, especially in the process of designing computer networks or retail systems. Compared to classical queueing models (started in the 20th century by Erlang), the current models are becoming more and more complex, taking into account new assumptions related to the character of arrival flows, the non-homogeneity of customers or non-identical servers, and possible limitations in their functioning. Investigations of such models require knowledge from many different fields of mathematics: probability theory,  stochastic processes, mathematical analysis, differential equations, discrete mathematics, and numerical methods. For obtaining results, we also use simulations constructed with the use of high-level programming languages or symbolic calculations with the help of computer algebra systems. This allows the cooperation of researchers from various scientific areas. Results of the research are additionally very practical as they allow us to calculate, in real systems, the necessary sizes of queues, the number of servers, memory buffer sizes, and expected loss probabilities. The impact of these is likely to grow dynamically in the future.

The aim of this Special Issue is to report recent research results on queueing systems and their applications in different fields, encourage interaction among the researchers investigating such models, discuss important research problems and new directions, and promote the use of different analysis methods in various research areas. We would like to invite researchers to submit their new findings on the areas mentioned above or related ones.

Topics to be covered:

• Classical queueing systems and their modifications;
• Queueing networks;
• Queueing systems with non-homogeneous customers;
• Queueing systems with non-identical servers;
• Queueing systems with vacations;
• Queueing systems with sectorized memory; 
• The use of matrix methods in the analysis of complicated queueing models;
• Numerical, algorithmic, approximation, and simulation methods in queueing systems analysis;
• Applications of queueing systems in real engineering or computer systems. 

Prof. Dr. Oleg Tikhonenko
Dr. Marcin Ziółkowski
Guest Editors

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• queueing model
• Markov chain
• loss probability
• Laplace transform
• non-homogeneous customers
• non-identical servers
• priority queue
• queues with vacations
• summary volume
• simulation methods