We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let (V(t))t≥0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let τn be his arrival time. In both models there is a capacity bound v* ∈(0, ∞). In Model I the amount of service given to the nth customer is equal to min[Sn, v*-V(τn-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(τn-) exceeds v*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods.
Bibliographical noteFunding Information:
This research was carried out while the first author (D. Perry) was a visiting professor at the University of Osnabrück. The support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
ASJC Scopus subject areas
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics