Title :
On the distribution of the time to buffer overflow in a queueing system with a general-type input stream
Author :
Kempa, Wojciech M.
Author_Institution :
Silesian Univ. of Technol., Gliwice, Poland
Abstract :
A finite-buffer queueing system with a generally distributed interarrival times and exponential service times is considered. A compact formula for the Laplace transform of distribution of the time to the first buffer overflow is found and written down using a special-type sequence connected with “input” distributions of the system. Moreover, applying the formula of total probability, a representation for the distribution of the time to the kth buffer overflow for k ≥ 2 is derived. Numerical examples are attached as well.
Keywords :
Laplace transforms; queueing theory; Laplace transform; buffer overflow; distributed interarrival times; exponential service times; finite buffer queueing system; general type input stream; probability; Distribution functions; Equations; Laplace equations; Markov processes; Mathematical model; Queueing analysis; Transforms; Buffer overflow period; Markov moments; finite-buffer queue; packet losses;
Conference_Titel :
Telecommunications and Signal Processing (TSP), 2012 35th International Conference on
Conference_Location :
Prague
Print_ISBN :
978-1-4673-1117-5
DOI :
10.1109/TSP.2012.6256283
