TY - BOOK
T1 - A blood bank model with perishable blood and demand impatience
AU - Bar-Lev, S.K.
AU - Boxma, O.J.
AU - Mathijsen, B.W.J.
AU - Perry, D.
PY - 2015
Y1 - 2015
N2 - 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 cancelled 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 Xb kept in storage, and of the amount of demand for blood Xd (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.
AB - 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 cancelled 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 Xb kept in storage, and of the amount of demand for blood Xd (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.
M3 - Report
T3 - Report Eurandom
BT - A blood bank model with perishable blood and demand impatience
PB - Eurandom
CY - Eindhoven
ER -