Spatial no-waiting stations with moving customers
We analyze spatial MAP/G/infinity-, spatial MAP/G/c/0(1) and spatial Cox/G/infinity-stations with group arrivals over some Polish space X (with Borel sigma-algebra X), including the aspect of customer motion in space. For models with MAP-input, characteristic differential equations are set up that describe the dynamics of phase dependent random functions Q(r); (ij) (u, t; S'), where Q(r; ij) (u, t; S') is the probability to observe, at time u less than or equal to t, the number r of those customers in some source set S' is an element of X, who will be in a destination set S is an element of X at time t. For Cox/G/infinity-stations, i.e., infinite server stations with doubly stochastic input, the arrival intensities as well as service times may depend on some general stochastic process (J(t)')(t)greater than or equal to0 with countable state space. For that case we obtain explicit expressions for space - time distributions as well as stationary and non-stationary characteristics.
customer motion spatial markovian arrival processes (smaps) smap/g/infinity- smap/g/c/0-and spatial cox/g/infinity stations with group arrivals mobile communication network analysis