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**Blocking when service is required from several facilities simultaneously.**
*(English)*
Zbl 0591.90035

Summary: This paper analyzes a mathematical model of a blocking system with simultaneous resource possession. There are several multiserver service facilities without extra waiting space at which several classes of customers arrive in independent Poisson processes. Each customer requests service from one server in each facility in a subset of the service facilities, with the subset depending on the customer class. If service can be provided immediately upon arrival at all required facilities, then service begins and all servers assigned to the customer start and finish together. Otherwise, the attempt is blocked (lost without generating retrials). The problem is to determine the blocking probability for each customer class. An exact expression is available, but it is complicated. Hence, this paper investigates approximation schemes.

### MSC:

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |