Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Stochastic monotonicity of the queue lengths in closed queueing networks
Operations Research
Simple bonds for finite single-server exponential tandem queues
Operations Research
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Product Form and Local Balance in Queueing Networks
Journal of the ACM (JACM)
A Characterization of Product-Form Queuing Networks
Journal of the ACM (JACM)
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Queuing networks with population size constraints
IBM Journal of Research and Development
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In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled.There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an M|G|c|c system and an upper bound by an M|G|c-1|c-1 system, hence by simple Erlang loss expressions.The result is based on a product form modification for a special OT---ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.