Title :
Tandem queueing system MAP|M|N|K - N → ●|M|R|∞ with impatient customers as a model of remote technical support
Author :
Dudin, Alexander ; Dudin, Sergey ; Dudina, Olga
Author_Institution :
Fac. of Appl. Math. & Comput. Sci., Belarusian State Univ., Minsk, Belarus
Abstract :
We consider a tandem queueing system with Markovian Arrival Process (MAP) as a model of remote technical support. The first stage is a multi-server queueing system with a finite buffer and impatient customers. After the service at the first stage the customer leaves the system or moves to the second stage. The second stage has a finite number of servers and an infinite buffer. The service time at the first and second stages has an exponential distribution with different parameters. The ergodicity condition is derived. A numerically stable algorithm for calculation of the stationary distribution of the system under consideration is presented. The main performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn time distribution at the both stages are derived.
Keywords :
Laplace transforms; Markov processes; buffer storage; exponential distribution; numerical stability; queueing theory; technical support services; Laplace-Stieltjes transform; MAP; Markovian arrival process; ergodicity condition; exponential distribution; impatient customer; infinite buffer; multiserver queueing system; numerically stable algorithm; remote technical support; service time; sojourn time distribution; stationary distribution; tandem queueing system; Generators; Markov processes; Mathematical model; Probability; Servers; Transforms; Vectors;
Conference_Titel :
Future Internet Communications (BCFIC), 2012 2nd Baltic Congress on
Conference_Location :
Vilnius
Print_ISBN :
978-1-4673-1672-9
DOI :
10.1109/BCFIC.2012.6217993
