Queueing theory and application of “queueing” library in R software

V diplomskem delu so predstavljeni osnovni elementi čakalnih vrst in uporaba programa R. Zaradi praktično vsakodnevnega srečevanja s čakalnimi vrstami je smiselno predstaviti osnovne pojme in procese čakalnih vrst. Zaposleni na področju “Podpore strankam” se velikokrat srečujejo s preobremenjenostjo in stresom, ki pa lahko posledično vodi v slabšo kakovost nudenja storitev. Da se ugotovi ali je model čakalne vrste ustrezen, je potrebna teorija čakalnih vrst ter analiza podatkov. V diplomskem delu je bil poudarek predvsem na enokanalni čakalni vrsti modela, kjer je vhodni proces kot tudi izhodni proces strank porazdeljen eksponentno, s predpostavko, da je zaključek časa strežbe porazdeljen po nekem splošnem porazdelitvenem zakonu. Čakalna vrsta je po Kendall-Leejevi notaciji zapisana kot M/M/1. V drugem delu diplomskega dela smo s pomočjo opisa dela podpore strankam na konkretnem primeru zasnovali model čakalne vrste. Ker se je ujemal z izbranim osnovnim teoretičnim modelom, smo lahko naredili primerjalno analizo s pomočjo programskega orodja R in knjižnice “queueing”, kjer je bil ponazorjen princip delovanja na simulacijskem primeru. Izvedla se je analiza pretoka strank pri delu “Podpora strankam” ter analiza v primeru večjega števila serverjev oziroma operaterjev. S pomočjo knjižnice ni bilo potrebno posebej definirati formul za izračun različnih parametrov, kar pa je pripomoglo k hitrejši in lažji analizi.This thesis deals with the basic elements of queues and the use of the software R for statistical calculations and graphics. Since people basically deal with queues on a daily basis, it is useful to introduce the basic meanings and processes of queues. People, who work as “Customer Support”, face work overload and stress due to the nature of their work, which can subsequently lead to poorer service quality. To find out whether the queuing model is appropriate, queuing theory and data analysis are required. In this thesis, we have mainly focused on a single-channel queuing model in which both the input and output processes of customer management are exponentially distributed, assuming that the time to the end of service is distributed according to a general distribution law. The queue is written as M/M/1 according to the Kendall-Lee notation. In the second part of the thesis, I developed a queueing model based on a description of my work as a "Customer Service Representative" in my previous job. Since it was consistent with the basic theoretical model chosen, we were able to perform a comparative analysis using the software R and the library "queueing", where the working principle of the above model was illustrated in a simulation example. Both an analysis of the customer flow at the "customer service" workstation and an analysis in the case of a larger number of servers or operators were performed. With the help of the library, it was not necessary to define special formulas for the calculation of the various parameters, which made the analysis faster and easier