Invariance of the stationary distribution of G-networks with bounded sojourn time with respect to service time distributions
EDN: YCAZVV
Abstract
We consider a queueing network with negative customers, single-server nodes, and constraints on the sojourn time of customers in nodes. If, at the moment a negative customer arrives at a node, there are positive customers present, one of the positive customers instantly disappears from the network. If, however, no positive customers are present in the node at that moment, the incoming negative customer vanishes immediately and has no further effect on the network’s behavior. Positive customers whose sojourn time in a node has expired instantly and independently of other positive customers begin routing according to a transition matrix that differs from the routing matrix used by positively served customers. The insensitivity of the stationary distribution to the shape of the service time distribution given fixed first moments is proven. The conditional distribution of customer sojourn times in nodes is exponential.
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Review
For citations:
Evmenenko S.Yu. Invariance of the stationary distribution of G-networks with bounded sojourn time with respect to service time distributions. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(2):114-120. (In Russ.) EDN: YCAZVV
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