Add analysis section to motivate the single server queue example

Doc/library/random.rst

@@ -426,25 +426,32 @@ between the effects of a drug versus a placebo::
 
 Simulation of arrival times and service deliveries in a single server queue::
 
-    from random import gauss, expovariate
+    from random import expovariate, gauss
+    from statistics import mean, median, stdev
 
     average_arrival_interval = 5.6
     average_service_time = 5.0
     stdev_service_time = 0.5
 
     num_waiting = 0
+    arrivals = []
+    starts = []
     arrival = service_end = 0.0
     for i in range(20000):
         if arrival <= service_end:
             num_waiting += 1
             arrival += expovariate(1.0 / average_arrival_interval)
-            print(f'{arrival:6.1f} arrived')
+            arrivals.append(arrival)
         else:
             num_waiting -= 1
             service_start = service_end if num_waiting else arrival
             service_time = gauss(average_service_time, stdev_service_time)
             service_end = service_start + service_time
-            print(f'\t\t{service_start:.1f} to {service_end:.1f} serviced')
+            starts.append(service_start)
+
+    waits = [start - arrival for arrival, start in zip(arrivals, starts)]
+    print(f'Mean wait: {mean(waits):.1f}.  Stdev wait: {stdev(waits):.1f}.')
+    print(f'Median wait: {median(waits):.1f}.  Max wait: {max(waits):.1f}.')
 
 .. seealso::