Wyniki wyszukiwania - BazTech

1

Performance evaluation of unreliable system with infinite number of servers

Tikhonenko O., Ziółkowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2020

|

Vol. 68, nr 2

289--297

EN

In the paper, we investigate queueing system M/G/∞ with non-homogeneous customers. By non-homogeneity we mean that each customer is characterized by some arbitrarily distributed random volume. The arriving customers appear according to a stationary Poisson process. Service time of a customer is proportional to his its volume. The system is unreliable, which means that all its servers can break simultaneously and then the repair period goes on for random time having an arbitrary distribution. During this period, customers present in the system and arriving to it are not served. Their service continues immediately after repair period termination. Time intervals of the system in good repair mode have an exponential distribution. For such system, we determine steady-state sojourn time and total volume of customers present in it distributions. We also estimate the loss probability for the similar system with limited total volume. An analysis of some special cases and some numerical examples are attached as well.

2

M/G/n/(0, V) Erlang queueing system with non-homogeneous customers, non-identical servers and limited memory space

Tikhonenko O., Ziółkowski M., Kurkowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2019

|

Vol. 67, nr 3

489--500

EN

In the present paper, we investigate a?multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a?stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.

3

M/G→ /n/0 Erlang queueing system with heterogeneous servers and non-homogeneous customers

Ziółkowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2018

|

Vol. 66, nr 1

59--66

EN

In the present paper, we investigate a multi-server queueing system with heterogeneous servers, unlimited memory space, and non-homogeneous customers. The arriving customers appear according to a stationary Poisson process. Service time distribution functions may be different for every server. Customers are additionally characterized by some random volume. On every server, the service time of the customer depends on their volume. The number of customers distribution function is obtained in the classical model of the system. In the model with non-homogeneous customers, the stationary total volume distribution function is determined in the term of Laplace–Stieltjes transform. The stationary first and second moments of a total customers volume are calculated. An analysis of some special cases of the model and some numerical examples are also included.

4

M/M/n/(m,V) queueing systems with a rejection mechanism based on AQM

Ziółkowski M., Małek J.

Journal of Applied Mathematics and Computational Mechanics

|

2013

|

Vol. 12, nr 1

121--130

EN

M/M/n/(m,V) queueing systems with service time independent of customer volume are well known models used in computer science. In real computer systems (computer networks etc.) we often deal with the overload problem. In computer networks we solve the problem using AQM techniques, which are connected with introducing some accepting function that lets us reject in random way some part of the arriving customers. It causes reduction of each customer's mean waiting time and let us avoid jams in consequence. Unfortunately, in this way the loss probability increases. In this paper we investigate the analogous model based on some generalization of M/M/n/(m,V) queueing system. We obtain formulas for a stationary number of customers distribution function and loss probability and we do some computations in special cases.