Stochastic Systems

A Blood Bank Model with Perishable Blood and Demand Impatience

Shaul K. Bar-Lev, Onno Boxma, Britt Mathijsen, and David Perry

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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.

Article information

Stoch. Syst., Volume 7, Number 2 (2017), 237-262.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]
Secondary: 60J60: Diffusion processes [See also 58J65] 33C15: Confluent hypergeometric functions, Whittaker functions, $_1F_1$

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. Stoch. Syst. 7 (2017), no. 2, 237--262. doi:10.1287/stsy.2017.0001.

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