qdata = [5, 5, 5, 6, 5, 6, 6, 7, 6, 5, 6, 5, 4, 5, 6, 6, 6, 7, 8, 7, 6, 6, 6, 5, 4, 4, 5, 5, 4, 5, 6, 6, 5, 4, 3, 3, 2, 2, 1, 2, 2, 3, 3, 2, 3, 4, 3, 2, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 6, 7, 6, 5, 4, 4, 3, 3, 2, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 2, 3, 4, 4, 3, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 2, 1, 2, 1, 2, 1, 2, 3, 4, 5, 5, 6, 5, 6, 5, 4, 4, 4, 3, 2, 2, 1, 2, 2, 3, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 1, 2, 3, 4, 3, 2, 1, 2, 3, 3, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 2, 1, 1, 1, 1, 2, 3, 4, 5, 6, 6, 7, 6, 5, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 0, 1, 1, 2, 2, 3, 2, 1, 2, 3, 2, 3, 4, 4, 4, 5, 6, 7, 6, 5, 4, 3, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 3, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 3, 2, 1, 2, 1, 1, 1, 2, 3, 4, 4, 3, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 5, 4, 4, 4, 4, 3, 2, 1, 1, 2, 2, 1, 1, 0, 1, 1, 2, 3, 2, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 2, 2, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 2, 2, 3, 2, 1, 1, 1, 1, 0, 0, 1, 0, 1, 2, 2, 1, 2, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 3, 3, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 4, 4, 4, 4, 3, 4, 4, 4, 5, 4, 5, 5, 5, 4, 3, 4, 4, 5, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 8, 8, 7, 7, 8, 9, 10, 11, 10, 11, 10, 9, 8, 8, 7, 8, 9, 8, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 6, 7, 8, 7, 7, 6, 5, 4, 4, 3, 3, 4, 5, 5, 4, 3, 2, 3, 4, 4, 4, 4, 4, 3, 3, 4, 5, 5, 6, 6, 6, 6, 6, 5, 5, 4, 4, 3, 2, 2, 1, 0, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 3, 2, 1, 2, 2, 3, 4, 4, 4, 5, 6, 5, 6, 7, 6, 6, 5, 4, 3, 3, 4, 4, 5, 4, 4, 5, 4, 3, 2, 2, 1, 0, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 4, 5, 4, 3, 3, 2, 3, 3, 3, 4, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 12, 11, 11, 10, 11, 11, 11, 10, 9, 9, 10, 10, 9, 8, 8, 7, 7, 6, 7, 8, 8, 8, 8, 7, 8, 7, 7, 6, 5, 6, 6, 6, 7, 8, 7, 7, 6, 6, 5, 5, 6, 7, 7, 7, 6, 7, 8, 9, 8, 7, 7, 6, 6, 6, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 15, 15, 16, 15, 14, 13, 14, 15, 14, 13, 14, 15, 15, 14, 14, 13, 14, 14, 15, 14, 15, 14, 13, 12, 12, 11, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16, 17, 18, 17, 17, 18, 19, 19, 18, 17, 16, 17, 18, 18]

language = python

Q.5 (*) A queue is observed over 10000 one-second time intervals with data as given below in the array adata. Construct a Poisson nearest neighbour model with a single arrival and servicing pattern and hence answer the following questions: 1. What is the average time taken for 1 customer to arrive? 2. What is the average number of customer servicings per second? 3. What is your estimate for the equilibrium probability P(n > 4), where n is the queue size in this model? 4. Suppose that two equivalent servers are introduced. What would the equilibrium probability P(n > 4) then be? [33]: qdata = [5, 5, 5, 6, 5, 6, 6, 7, 6, 4, 5, 6, 6, 6, 7, 8, 7, 6, 6, 6, 5, 4, 4, 5 5, 4, 5, 6, 6, 5, 4, 3, 3, 2, 2 [34]: len(data) [34]: 10001 [ ]: []: [ ]: [ ]: [ ]: []: Q.5 (*) A queue is observed over 10000 one-second time intervals with data as given below in the array adata. Construct a Poisson nearest neighbour model with a single arrival and servicing pattern and hence answer the following questions: 1. What is the average time taken for 1 customer to arrive? 2. What is the average number of customer servicings per second? 3. What is your estimate for the equilibrium probability P(n > 4), where n is the queue size in this model? 4. Suppose that two equivalent servers are introduced. What would the equilibrium probability P(n > 4) then be? [33]: qdata = [5, 5, 5, 6, 5, 6, 6, 7, 6, 4, 5, 6, 6, 6, 7, 8, 7, 6, 6, 6, 5, 4, 4, 5 5, 4, 5, 6, 6, 5, 4, 3, 3, 2, 2 [34]: len(data) [34]: 10001 [ ]: []: [ ]: [ ]: [ ]: []