Bendigo Health is a 672-bed hospital near Melbourne, Australia.8 When the hospital admin-istrators wanted to decide on tire number of beds to set aside for a new program, transition care, some research staff suggested the use of queuing theory. Some hospital patients would qualify for the option of transition care before a group/nursing home is found for them. It is estimated that an average of λ = 1.2 patients per week would be eligible and interested for transition care (Poisson distribution). The average stay in transition care is estimated to be (1/μ,) = 9.5 weeks. If a bed is not available in transition care, the patient leaves for another facility (i.e., there is no wait). The research staff suggested the following method: first assume that the number of beds in transition care is infinite. Then, determine the average occupancy (i.e., the average number of patients in the system) = 1.2 (9.5) = 11.4. Finally, us e the fact that the distribution of number of patients in the system is Poisson with a mean of 11.4 to determine the probability that a bed will not be used, given various maximum number of beds. For example, €œif the hospital allocates 9 beds to transition care, then in the long run there would be some empty beds on 19.84% of days, or about I day in 5.€
a. Use Excel to verify the 19.84% result. Note that the Poisson table at the end of the textbook goes up to only a mean of 9.5.
b. An alternative method is to use the following (Erlang B) formula,9 where pn = probability of n patients in the system and K = maximum number of beds.

Which method is more appropriate for this problem?

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μ. n! Pn = ΣΑ j! μ.