Scenario :

The internal medicine department unit serves a large catchment area comprised of a significantly older population. Due to budget constraints and resourcing issues, it can only afford to have six medical staff service the outpatient department per day.

Recently, the head of the department has approached the hospital Chief Executive Officer (CEO) to fund additional medical staff noting that not only is the unit treating a growing number of medical presentations, but also that a small hospital nearby is closing, which will result in the department needing to pick up the resulting increase in patient load.

The CEO approaches you, the operations manager, to assist them in considering this request. In your activities to assist the CEO, you need to consider the burden on the unit in different scenarios. For your calculations you consider using the M/M/s/b model as the outpatient unit employs an FCFS/single line/multiple server's model.

Data: The department provides you with the following:

? Arrival rate: 20 patients per hour

? Service rate: 10 patients per hour

? Number of servers: 6 medical staff

? Waiting room size: 14 patients

The department head advises you that this data did not include situations where there is an increased number of patient arrivals based on the burden of increasing chronic disease in the community and the impending closure of the nearby hospital, which will lead to increasing numbers of patients.

You work with the department to arrive at a projected patient arrival rate based on these scenarios, which is now 65 patients per hour. You will now need to input and update this new data into your spreadsheet to recalculate your results.

Your task Referencing the two data sets and drawing on your calculations, address the following questions :

? What parameters in both scenarios led to your decision?

? Why were they considered?

? What made you reconsider your decision?

As part of your submission, discuss the second scenario and the impact on the rest of the hospital (inpatient) in the context of your learning so far (i.e. patient flow, waiting time, delay and queuing theory).

First scenario :

M/M/s/b queue Multiple servers, Infinite population, Poisson arrival, FCFS, Exponential service time, Limited capacity (b) Inputs Unit of time Hour Arrival rate (2) 20 patients per Hour Service rate (J) 10 patients per Hour Number of servers (s) 6 Hospital staff (Note: The maximum capacity in system Buffer (waiting room) size 14 patients equal to number of servers plus waiting Outputs Mean time between arrivals 0.050 Hour Mean time per service 0.1 Hour Traffic intensity 0.333333333 Summary measures Average utilization rate of servers 33.3% Average number of customers waiting in line (nl) 0.0090 patients Average number of customers in system (ns) 2.0090 patients Average time waiting in line (tl) 0.0005 Hour Average time in system (ts) 0. 1005 Hour Probability of no customers in system (PO) 0. 1351 (Probability of empty system) Probability of rejecting a customer (balking rate) 0.00% (Reject rate) Effective arrival rate 19.99999995 (Entering rate)sth queue 'Multiple sewers, lntinite population, Poisson arrival, IFCFS, Exponential service time, Limited capacity (b) Inputs _ _Unit of time Hour Arrival rate [1] 65 patients per Hour Service rate (u) 10 patients per Hour Number of servers (s) 6 Hospital staff (Note: The maximum capacity in system is _ Buffer [waiting room} size 14 patients equal to number of servers plus waiting room size) _ Outputs Mean time between arrivals Hour Mean time per service Hour Traflic intensity I _| Summary measures _Average utilization rate of servers 91% Average number of customers waiting in line [nl] 1m: patients Average number of customers in system [ns] 1.1% patients Average time waiting in line {ti} mm Hour _Average time in system (ts) am Hour Probability of no customers in system [P0] 0mm [Probability of empty system} Probability of rejecting a customer (balking rate} 13.1596 {Reject rate) Effective arrival rate $101M [Entering rate}