Coloquiodo Depto. de Estatistica/UNICAMP

[ronaldo <dias@ime.unicamp.br>]

Prezados(as) Colegas:

   Dando inicio ao Coloquio do Depto. de Estatistica-IMECC, teremos a 
presenca do Prof.. Menshikov que apresentara  seminario no dia 24/08/07 
as 10hs., sala 221. Titulo e resumo seguem abaixo.

   Novamente, contamos com sua presenca. Obrigado,

ronaldo

PS. Proximo seminario em Setembro. Convidado: Prof. Jorge A. Achcar.

----------------------TITULO e RESUMO 
---------------------------------------

Título:
Polling systems with random changes of regime

Resumo:
We study a model of a polling system i.e.\ a collection of $d$
queues with a single server that switches from queue to queue. Only
two queues are \emph{open} to arriving jobs at any time with the
server at one of them. When the server completes all jobs at its
current queue several things happen: its current queue closes; the
server starts to switch to the other open queue; another queue
opens. The queue to open is chosen so that the sequence of queues
visited by the server forms a Markov chain.  The open queues receive
Poisson streams of jobs and service times are independent with
general distribution.  The arrival rates at the open stations and
the service distribution are re-set randomly each time the server
switches to a new station.  Each switching event takes a random time
that may depend upon which queues are open. Let $\tau$ denote the
time required to empty the system. We give explicit conditions for
when $\tau$ is a.s.\ finite and for any $s > 0$ whether ${\bf E}(\tau^s)
< \infty$ or not. In proving our results we consider a
multiplicative random walk of independent interest for which we also
give explicit stability and transience criteria.