I need to build an Excel simulation regarding a single lane bridge crossing to determin $$the $$impact $$that $$three $$diffrent $$crossing methods has on vehicle wait time.

The assumptions are as follows:

$-$Northbound traffic arrives at the bridge at a rate of $3\mathrm{.}5$ vehicles per minute.

$-$Southbound traffic arrives at the bridge at a rate of $4$ vehicles per minute.

The arrival rate is exponentially distributed for both directions.

$-$Traversing the bridge takes between $10-20$ seconds with the time interval being equally likely withen this range.

$-$If vehicles travel back to back in the same direction, $3$ seconds is added to the crossing per vehicle.

Method one:

One group of bridge users believed that the bridge should alternate vehicles. That is$,$ the first vehicle to arrive at the bridge should cross first. If$,$ immediately after this vehicle had crossed, there was a vehicle waiting to cross from the opposite direction $,$ then this vehicle had priority. If there was a queue of vehicles at either end of the bridge, then traffic on the bridge would switch direction after each vehicle.

Method two:

A second group of users believed that traffic on the bridge should stay in the same direction until there were no more vehicles to cross. Once the bridge was free, vehicles traveling in the opposite direction could $$capture$$ the bridge until the entire queue had crossed $($by which time there would likely be a new queue of vehicles coming from the other direction$).$

Method three:

A third group of bridge users suggested that the only $$fair$$ discipline was strict $$first to arrive, first to cross$$: vehicles should cross the bridge in strict order of their arrival at the bridge, regardless of direction.