142 The UMAP Journal 28.2(2007) lifetime with the transplant is greater. Children below 11 years of age get 4 additional points, and those between 11 and 18 get 3 additional points. o hla mismatch points Because there are two chromosomes, the possible number m of mismatches in the donor-recipient( DR) locus of the hla se quence is 0, 1, or 2. A candidate-donor pair gets 2-m points Model Setup Wemodel theentry and exit of candidates from the waitlistwitha continuous- time Markov birth/ death process [Ross 2002]. It accommodates reduction of the waitlist size(arrivals of living donors and deceased donors and deaths and recoveries of waitlist candidate)and waitlist additions. o In 2006, 29, 824 patients were added to the kidney transplant waitlist, while 5,914 transplants had living donors, so 5914/(29824+ 5914)N% of in- coming patient cases have a willing compatible living donor. o The procedure for allocating deceased-donor kidneysis [Organ Procurement .2006,353-16f: First, match the donor blood type with compatible recipient blood types. exceptions are, Type O donors must be donated to type O recipients first, and Type B donors must be donated to type B recipients first Perfect matches(same blood type and no HLA mismatch)receive first If a kidney with blood type O or B has no perfect-matching candidates in the above procedure, then the pool is reopened for all candidates In the 17% of cases of no a perfect match with any recipient [wikipedia 2007, then sort by PRa value(higher priority to high PRA; high PRA long time), then atibility, which likely means being on the waitlist for a means low c by regional location of the kidney, then by points in the oint allocation system Summary of Markov process Let N, be a random variable indicating the number of people in the waitlist at time t. The properties of N can be generalized in Figure 1, where o Each arrow represents a possible event at the current state(N). o The rate at which each event occurs is exponentially distributed.142 The UMAP Journal 28.2(2007) lifetime with the transplant is greater. Children below 11 years of age get 4 additional points, and those between 11 and 18 get 3 additional points. e HLA mismatch points Because there are two chromosomes, the possible number m of mismatches in the donor-recipient (DR) locus of the I-ILA se￾quence is 0, 1, or 2. A candidate-donor pair gets 2 - m points. Model Setup We model the entry and exit of candidates from the waitlist with a continuous￾time Markov birth/death process [Ross 2002]. It accommodates reduction of the waitlist size (arrivals of living donors and deceased donors and deaths and recoveries of waitlist candidate) and waitlist additions. "* In 2006, 29,824 patients were added to the kidney transplant waitlist, while 5,914 transplants had living donors, so 5914/(29824 + 5914) ;-, 17% of in￾coming patient cases have a willing compatible living donor. "* The procedure for allocating deceased-donor kidneys is [Organ Procurement ... 2006, 3.5, 3-16ff]: - First, match the donor blood type with compatible recipientblood types. The only exceptions are: * Type 0 donors must be donated to type 0 recipients first, and: * Type B donors must be donated to type B recipients first. - Perfect matches (same blood type and no I-ILA mismatch) receive first priority. - If a kidney with blood type 0 or B has no perfect-matching candidates in the above procedure, then the pool is reopened for all candidates. - In the 17% of cases of no a perfect match with any recipient [Wikipedia 20071, then sort by PRA value (higher priority to high PRA; high PRA means low compatibility, which likely means being on the waitlist for a long time), then by regional location of the kidney, then by points in the point allocation system. Summary of Markov Process Let Nt be a random variable indicating the number of people in the waitlist at time t. The properties of Nt can be generalized in Figure 1, where "* Each arrow represents a possible event at the current state (N). "* The rate at which each event occurs is exponentially distributed