TY - GEN
T1 - Output process in batch-arrival queue with N-policy and multiple vacations
AU - Kempa, Wojciech M.
PY - 2013
Y1 - 2013
N2 - In the paper the MX/G/1-type queueing system with the N-policy and multiple vacations is considered. The output process, counting successive departures, is studied using the approach consisting of two main stages. Firstly, introducing an auxiliary model with the N-policy and multiple vacations, and applying the formula of total probability, the analysis is brought to the case of the corresponding system without restrictions in the service process, on its first busy cycle. Next, defining a delayed renewal process of successive vacation cycles, the general results are obtained. The explicit formula for the probability generating function of the Laplace transform of the distribution of the number of packets completely served before a fixed moment t is derived and written using transforms of "input" distributions of the system, and components of the Wiener-Hopf-type factorization identity connected with them. Moreover, illustrative numerical results are presented.
AB - In the paper the MX/G/1-type queueing system with the N-policy and multiple vacations is considered. The output process, counting successive departures, is studied using the approach consisting of two main stages. Firstly, introducing an auxiliary model with the N-policy and multiple vacations, and applying the formula of total probability, the analysis is brought to the case of the corresponding system without restrictions in the service process, on its first busy cycle. Next, defining a delayed renewal process of successive vacation cycles, the general results are obtained. The explicit formula for the probability generating function of the Laplace transform of the distribution of the number of packets completely served before a fixed moment t is derived and written using transforms of "input" distributions of the system, and components of the Wiener-Hopf-type factorization identity connected with them. Moreover, illustrative numerical results are presented.
KW - Batch-arrival queueing system
KW - N-policy
KW - multiple vacations
KW - output process
KW - transient state
UR - https://www.scopus.com/pages/publications/84884972023
U2 - 10.1007/978-3-642-39408-9_18
DO - 10.1007/978-3-642-39408-9_18
M3 - Conference contribution
AN - SCOPUS:84884972023
SN - 9783642394072
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 247
EP - 261
BT - Analytical and Stochastic Modelling Techniques and Applications - 20th International Conference, ASMTA 2013, Proceedings
T2 - 20th International Conference on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2013
Y2 - 8 July 2013 through 10 July 2013
ER -