Year: 2025
Type: article
Abstract: We consider a single-server two-queue Markovian polling system with the following special feature. If the server is serving the infinite-buffer queue $$Q_2$$ Q 2 and the single-buffer queue $$Q_1$$ Q 1 is empty, then it stays at $$Q_2$$ Q 2 until it has become empty; but if a customer joins an empty $$Q_1$$ Q 1 , then the server only stays at $$Q_2$$ Q 2 as long as that queue has at least N customers (the threshold). If that customer joins $$Q_1$$ Q 1 while $$Q_2$$ Q 2 has less than N customers, then service at $$Q_2$$ Q 2 is preempted and the server instantaneously switches to $$Q_1$$ Q 1 . Arrivals to $$Q_1$$ Q 1 when it is occupied are blocked and lost. This threshold discipline contrasts with the classical multi-queue polling model, where switching instants are typically determined by the length of the queue being served. We (i) derive explicit expressions for the joint queue length distribution; (ii) analyze the busy period distribution by employing an original approach that uses taboo states; and (iii) determine the sojourn time distribution for customers in both queues.
Source: Queueing Systems
Authors: Onno Boxma, David Perry, Rachel Ravid, Uri Yechiali
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4415246177