THE CONDITIONAL LAW OF A M/M/1 QUEUE WITH
RESPECT TO ITS DEPARTURE PROCESS AND IDLE TIME
Barbara Torti
Dipartimento di Matematica
Universita di Roma Tor Vergata
Via della Ricerca Scientifica, 1 00133 Roma, ITALY
Abstract. A filtering problem is considered in the case when the state process is a M/M/1 queue Qt and the observation process is the pair of its idle time and departure process. An explicit construction of the filter is given.
AMS Subject classification: 60K20, 93E11, 60G55
Keywords and phrases: queues, idle time, nonlinear filtering, point processes


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DOI: 10.12732/ijam.v27i5.5

Volume: 27
Issue: 5
Year: 2014