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 A blood bank model with perishable blood and demand impatience
 Shaul K. Bar-Lev, University of HaifaOnno Boxma, Eindhoven University of TechnologyBritt Mathijsen, Eindhoven University of TechnologyDavid Perry, University of Haifa

 Abstract 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 $$X_b$$ kept in storage, and of the amount of demand for blood $$X_d$$ (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. AMS 2000 subject classifications: Primary 60K30; secondary 60J60, 33C15.Keywords: Blood bank, level-crossings, shot-noise model, confluent hypergeometric functions, scaling limits, Ornstein-Uhlenbeck process.
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Bar-Lev, Shaul K., Boxma, Onno, Mathijsen, Britt, Perry, David, A blood bank model with perishable blood and demand impatience, Stochastic Systems, 7, (2017), 1-46 (electronic). DOI: 10.1214/15-SSY197.

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