Stationary Stochastic Models.

Recursive stochastic equations - weak and strong solutions - ergodic weak solutions - construction of stationary weak and strong solutions - Wald's identity for dependent random variables - model continuity in the presence of renewing epochs - method of metric modification - continuity of weak solutions the case of stationary Markov chains stationary sequences and stationary marked point processes - ergodic marked point processes continuous time models - stochastic processes with an embedded point process - semi-Markov and semi-regenerative processes - continuous time state processes - recursive stochastic equations in continuous time arrival-stationary queuing processes: existence and uniqueness - notations - the system - single server queue - the system with FCFS queueing discipline - the system with cyclic queueing discipline - the single server queue with warming-up - the many server loss system with repeated call attempts - open networks of loss systems relationships between arrival, time and departure stationary queueing processes - Poisson arrivals see time averages (PASTA) - the number of customers - the busy cycle - Takaes' and Pollaczek-Khinchin formulae batch-arrival stationary queuing processes - the system with geometrically distributed batch size - constant batch size - single server queue with batch arrivals - feedback queues - comparing batch delays and customer delays continuity of queueing models further models - the stochastic equation with stationary coefficients - stability of robust filter cleaners - non-contractivity of the filters - a further method for constructing solutions of recursive stochastic equations - the filter with fixed scale - variable scale.