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Q2 25P Queuing A highway bridge is partially shut down to do some maintenance roadwork. Instead of having full three lanes, only one lane is now open so that workers can carry on their activities with safety from the passing traffic. In fact, such a 'bottleneck' commonly creates a queue in front of the roadwork. This can roughly be modelled as a M/C/1 system, traffic arriving in a Poisson like pattern forming a potentially infinite queue, and then passing the site of the roadwork in a steady pass one after one with a fixed speed and safe fixed distance between the vehicles on a single lane. Cars usually arrive to the bridge at a rate on 18 car/min in a Poisson like pattern. Cars go over at a steady slow pace with an even minimal safe distance between, at a rate of 1 car every 3rd second. 1. a) The queue is now 10 cars long in front of the bridge. Is this an unusually long queue? 2. b) How long time will the car arriving to this queue, as it is right now, have to wait until it can pass the bridge? 3.c) What happens to the characteristics of the outflow from a M/C/1 system in which inflow is displaying high variance (assume Poisson like distribution) when the capacity of the system approaches its full utilization (that is capacity equals the average flow rate)? 4. d) What is the advantages and disadvantages of applying such a setup in a LEAN production system? 03 Forecasting 25P