Open Access
2017 A Blood Bank Model with Perishable Blood and Demand Impatience
Shaul K. Bar-Lev, Onno Boxma, Britt Mathijsen, David Perry
Stoch. Syst. 7(2): 237-262 (2017). DOI: 10.1287/stsy.2017.0001


We consider a stochastic model for a blood bank, in which amounts of blood are offered and demanded according to independent compound Poisson processes. Blood is perishable, i.e., blood can only be kept in storage for a limited amount of time. Furthermore, demand for blood is impatient, i.e., a demand for blood may be canceled if it cannot be satisfied soon enough. For a range of perishability functions and demand impatience functions, we derive the steady-state distributions of the amount of blood kept in storage, and of the amount of demand for blood (at any point in time, at most one of these quantities is positive). Under certain conditions we also obtain the fluid and diffusion limits of the blood inventory process, showing in particular that the diffusion limit process is an Ornstein-Uhlenbeck process.


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Shaul K. Bar-Lev. Onno Boxma. Britt Mathijsen. David Perry. "A Blood Bank Model with Perishable Blood and Demand Impatience." Stoch. Syst. 7 (2) 237 - 262, 2017.


Received: 1 July 2015; Accepted: 1 May 2017; Published: 2017
First available in Project Euclid: 24 February 2018

zbMATH: 06849801
MathSciNet: MR3741353
Digital Object Identifier: 10.1287/stsy.2017.0001

Primary: 60K30
Secondary: 33C15 , 60J60

Keywords: blood bank , confluent hypergeometric functions , level-crossings , Ornstein-Uhlenbeck process , scaling limits , shot-noise model

Vol.7 • No. 2 • 2017
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