Trauma center moves to diversion status once all servers are busy (incoming patients are directed to other locations) Figure 7.1.: Process flow diagram for trauma center 3 trauma bays

Figure 7.2.: Implied utilization vs probability of having all servers utilized Implied utilization Probability that all servers are utilized m=1 m=2 m=5 m=10 m= m=3

Figure 7.4.: Impact of waiting time on customer loss Average wait time [seconds] Fraction of customer lost

Inflow Figure 7.5.: A serial queuing system with three resources Outflow Outflow of resource 1 = Inflow of resource 2 UpstreamDownstream

Inflow Figure 7.6.: The concepts of blocking and starving Outflow Activity completed Outflow Resource is blocked Inflow Resource is starved Activity not yet completed Empty space for a flow unit Space for a flow unit with a flow unit in the space

Figure 7.7.: Flow rate compared at four configurations of a queuing system Sequential system, no buffers Cycle time=11.5 minutes Sequential system, one buffer space each Cycle time=10 minutes (1) Sequential system, unlimited buffers Cycle time=7 minutes; inventory “explodes” Horizontally pooled system Cycle time=19.5/3 minutes=6.5 minutes 6.5 min/unit7 min/unit6 min/unit 6.5 min/unit7 min/unit6 min/unit 6.5 min/unit7 min/unit6 min/unit 3 resources, 19.5 min/ unit each

Waiting problem Loss problem Pure waiting problem, all customers are perfectly patient. All customers enter the process, some leave due to their impatience Customers do not enter the process once buffer has reached a certain limit Customers are lost once all servers are busy Same if customers are patientSame if buffer size=0 Same if buffer size is extremely large Figure 7.8.: Different types of variability problems