An introduction of stochastic models of single-channel queueing systems for the purpose of logistics and transport

V diplomskem delu so predstavljeni osnovni elementi delovanja sistemov množične strežbe s poudarkom na enokanalnih sistemih v logistiki in prometu. Najpogostejši problem omenjenih sistemov je generiranje čakalnih vrst, kar vpliva na zadovoljstvo uporabnikov in ponudnikov. Predstavljeni so temeljni principi, kako lahko z razvojem analitičnih modelov tovrstnih sistemov pripomoremo k njihovi temeljiti analizi in možnim izboljšavam sistemov množične strežbe. Vsak ponudnik storitev namreč strmi k čim boljšim rezultatom dela, zaradi česar se mora stalno prilagajati potrebam trga. V prvem delu raziskave smo se omejili na seznanitev nekaterih osnovnih pojmov verjetnosti in stohastičnih procesov, saj so ti nujno potrebni za razumevanje teorije množične strežbe. Nato smo spoznali t.i. Poissonov proces in izpeljali njegove značilnosti. Le-ta je zelo pomemben, kajti na njegovih principih temeljijo tako lastnosti rojstno-smrtnih sistemov kot tudi ena izmed praktičnih inačic teh sistemov, to so sistemi množične strežbe. V drugem delu raziskave je princip delovanja obravnavanih sistemov ponazorjen tudi na dveh simulacijskih primerih, ki sta bila izvedena s pomočjo programskega orodja Matlab. Nazorno je predstavljeno, kako spremembe intezivnosti zaključkov strežbe dokaj občutno vplivajo na obnašanje opazovanih statističnih značilk.In the dissertation the basic elements of the functioning of queueing systems are presented with emphasis on one-channel systems in logistics and transport. The most common problem of the mentioned systems is creating of waiting lines, which influences the satisfaction of users and providers. The basic principles of how development of analytical models of this kind of systems can contribute to their thorough analysis and possible improvements are presented. Every provider aims to achieve the best possible work results and that is why they must constantly adapt to market needs. In the first part of the research some basic terms about probability and stochastic processes are presented because of their importance for understanding the theory of queueing systems. Then the Poisson Process and all its characteristics are presented. This process is very important because the characteristics of Birth and Death systems as well as one of the practical variants of those systems, the mass service system, are based on its principles. In the second part of the research the functioning principle of the discussed systems is illustrated in two simulation examples that were performed with the help of Matlab software. It is clear that the changes of the service completion intensity influence the behaviour of the observed statistical characteristics