TY - GEN
T1 - Stability of a retrial queueing network with different classes of customers and restricted resource pooling
AU - Kim, Bara
PY - 2010
Y1 - 2010
N2 - We consider a retrial queueing network with different classes of customers and several servers. Each customer class is associated with a set of servers who can serve the class of customers. Customers of each class exogenously arrive according to a Poisson process. If an exogenously arriving customer finds upon his arrival any idle server who can serve the customer class, then he begins to receive a service by one of the available servers. Otherwise he joins the retrial group, and then tries his luck again after exponential time, the mean of which is determined by his customer class. Service times of each server are assumed to have general distribution. The retrial queueing network can be represented by a Markov process, with the number of customers of each class, and the customer class and the remaining service time of each busy server. Using the fluid limit technique, we find a necessary and sufficient condition for the positive Harris recurrence of the representing Markov process. This work is the first that applies the fluid limit technique to a model with retrial phenomenon.
AB - We consider a retrial queueing network with different classes of customers and several servers. Each customer class is associated with a set of servers who can serve the class of customers. Customers of each class exogenously arrive according to a Poisson process. If an exogenously arriving customer finds upon his arrival any idle server who can serve the customer class, then he begins to receive a service by one of the available servers. Otherwise he joins the retrial group, and then tries his luck again after exponential time, the mean of which is determined by his customer class. Service times of each server are assumed to have general distribution. The retrial queueing network can be represented by a Markov process, with the number of customers of each class, and the customer class and the remaining service time of each busy server. Using the fluid limit technique, we find a necessary and sufficient condition for the positive Harris recurrence of the representing Markov process. This work is the first that applies the fluid limit technique to a model with retrial phenomenon.
KW - Fluid limit
KW - Positive Harris recurrence
KW - Resource pooling
KW - Retrial queue
KW - Stability
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U2 - 10.1145/1837856.1837870
DO - 10.1145/1837856.1837870
M3 - Conference contribution
AN - SCOPUS:77956254107
SN - 9781450302128
T3 - 5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings
SP - 87
EP - 93
BT - 5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings
T2 - 5th International Conference on Queueing Theory and Network Applications, QTNA 2010
Y2 - 24 July 2010 through 26 July 2010
ER -