We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On ergodicity conditions in a polling model with Markov modulated input and state-dependent routing.
- Authors
Zorine, Andrei
- Abstract
A polling system with switchover times and state-dependent server routing is studied. Input flows are modulated by a random external environment. Input flows are ordinary Poisson flows in each state of the environment, with intensities determined by the environment state. Service and switchover durations have exponential laws of probability distribution. A continuous-time Markov chain is introduced to describe the dynamics of the server, the sizes of the queues and the states of the environment. By means of the iterative-dominating method a sufficient condition for ergodicity of the system is obtained for the continuous-time Markov chain. This condition also ensures the existence of a stationary probability distribution of the embedded Markov chain at instants of jumps. The customers sojourn cost during the period of unloading the stable queueing system is chosen as a performance metric. Numerical study in case of two input flows and a class of priority and threshold routing algorithms is conducted. It is demonstrated that in case of light inputs a priority routing rule doesn't seem to be quasi-optimal.
- Subjects
MARKOV processes; QUEUING theory; ROUTING algorithms; ITERATIVE methods (Mathematics); MATHEMATICAL statistics; QUEUEING networks
- Publication
Queueing Systems, 2014, Vol 76, Issue 2, p223
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-013-9385-3