Question: qdata = [4, 5, 6, 6, 6, 7, 6, 7, 6, 5, 4, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 5,

qdata = [4, 5, 6, 6, 6, 7, 6, 7, 6, 5, 4, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3,

qdata = [4, 5, 6, 6, 6, 7, 6, 7, 6, 5, 4, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 1, 2, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 7, 6, 7, 6, 6, 5, 4, 5, 4, 3, 2, 3, 2, 3, 2, 3, 2, 1, 1, 2, 3, 3, 4, 5, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 3, 4, 3, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 0, 0, 1, 1, 2, 3, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 5, 6, 7, 7, 6, 5, 4, 3, 4, 3, 3, 4, 3, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 3, 2, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 2, 3, 2, 3, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 0, 0, 1, 2, 3, 2, 3, 2, 2, 3, 4, 4, 5, 4, 3, 2, 3, 2, 3, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 3, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 2, 1, 0, 1, 2, 1, 2, 3, 4, 4, 3, 2, 2, 1, 2, 3, 4, 5, 4, 4, 5, 4, 3, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 4, 5, 6, 5, 6, 5, 4, 5, 6, 7, 6, 5, 6, 6, 7, 6, 7, 7, 6, 7, 6, 5, 4, 5, 5, 4, 5, 6, 6, 5, 6, 5, 6, 5, 6, 5, 5, 5, 4, 3, 4, 5, 6, 5, 4, 3, 3, 4, 3, 2, 3, 2, 3, 3, 2, 1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 3, 2, 3, 4, 5, 6, 7, 7, 8, 9, 8, 9, 8, 7, 6, 5, 5, 4, 5, 4, 3, 2, 1, 0, 1, 2, 1, 2, 3, 4, 5, 6, 7, 7, 8, 7, 8, 9, 8, 7, 6, 5, 4, 3, 4, 3, 4, 4, 5, 4, 3, 4, 3, 2, 3, 2, 3, 3, 2, 1, 1, 0, 1, 2, 1, 2, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 0, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 3, 2, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 7, 7, 6, 7, 8, 8, 9, 10, 9, 10, 9, 10, 11, 10, 9, 8, 9, 10, 11, 10, 10, 9, 10, 10, 9, 8, 7, 8, 9, 10, 9, 8, 7, 6, 7, 6, 7, 6, 5, 4, 4, 5, 4, 3, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 3, 2, 2, 2, 1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 3, 2, 3, 4, 5, 5, 4, 3, 4, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 3, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 3, 4, 3, 2, 1, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 4, 5, 6, 7, 6, 7, 7, 6, 5, 4, 3, 4, 3, 2, 2, 3, 4, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 2, 1, 2, 3, 2, 1, 0, 0, 0, 0, 1, 1, 2, 3, 2, 3, 2, 3, 4, 5, 6, 5, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 0, 0, 1, 2, 3, 2, 3, 2, 3, 3, 4, 3, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 0, 0, 0, 1, 2, 2, 3, 3, 2, 3, 4, 3, 2, 1, 2, 3, 3, 2, 1, 0, 1, 2, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 5, 4, 5, 4, 3, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 3, 2, 1, 0, 1, 2, 3, 4, 4, 3, 4, 3, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 3, 3, 4, 3, 2, 3, 2, 1, 0, 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 1, 0]

language = python

Restart the kernel Q.4 (*) A queue is observed over 1000 time intervals where the size of the queue after each time step is given. Construct a simple model for this queue as a Markov chain with only nearest neighbour interactions. 1. What is the expected behaviour of the queue as time continues? 2. Is the system ergodic? Leo? 3, 4, 4, 3, [26]: data = [4, 5, 6, 6, 6, 7, 6, 7, 6, 5, 4, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 1, 2, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 7, 6, 7, 6, 6, 5, 4, 5, 4, 3, 2, 3, 2, 3, 2, 3, 2, 1, 1, 2, 3, 3, 4, 5, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 3, 4, 3, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 0, 0, 1, 1, 2, 3, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 5, 6, 7, 7, 6, 5, 4, 3, 4, 3, 3, 4, 3, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 3, 2, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 2, 3, 2, 3, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 0, 0, 1, 2, 3, 2, 3, 2, 2, 3, 4, 4, 5, 4, 3, 2, 3, 2, 3, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1 aaa 1, 2, 2, 3, 2, 3, 4, 5, 6, 5, 6, 5, 4, 5, 6, 7, 6, 5, 6, 6, 7, 6, 7, 7, 6, 7, 6, 5, 4, 5, 5, 2, 2, 1, 2, 3, 45, 4a, 1, 1, 1, 2, 4, 5, 6, 6, 5, 6, 5, 6, 5, 6, 5, 5, 5, 4, 3, 4, 5, 6, 5, 4, 3, 3, 4, 3, 2, 3, 2, 3, 3, 2, 1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 3, 2, 3, 4, 5, 6, 7, 7, 8, 9, 8, 9, 8, 7, 6, 5, 5, 4, 5, 4, 3, 2, 1, 0, 1, 2, 1, 2, 3, 4, 5, 6, 7, 7, 8, 7, 8, 9, 8, 7, 6, 5, 4, 3, 4, 3, 4, 4, 5, 4, 3, 4, 3, 2, 3, 2, 3, 3, 2, 1, 1, 6, 1 1, 2, 1, 2, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 0, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 3, 2, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 7, 7, 6, 7, 8, 8, 9, 10, 9, 10, 9, 10, 11, 10, 9, 8, 9, 10, 11, 10, 10, 9, 10, 10, 9, 8, 7, 8, 9, 10, 9, 8, 7, 6, 7, 6, 7, 6, 5, 4, 4, 5, 4, 3, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 3, 2, 2, 2, 1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 3, 2, 3, 4, 5, 5, 4, 3, 4, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 3, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 3, 4, 3, 2, 1, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 4, 5, 6, 7, 6, 7, 7, 6, 5, 4, 3, 4, 3, 2, 2, 3, 4, 3, 4, 3, 2, 1, 8, 9, 1, 2, 3, 2, 1, 2, 3, 2, 1, 0, 0, 0, 0, 1, 1, 2, 3, 2, 3, 2, 3, 4, 5, 6, 5, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 0, 0, 1, 2, 3, 2, 3, 2, 3, 3, 4, 3, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 0, 0, 0, 1, 2, 2, 3, 3, 2, 3, 4, 3, 2, 1, 2, 3, 3, 2, 1, 0, 1, 2, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 5, 4, 5, 4, 3, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0. 1. 2. 2. 3. 2. 1. 0. 1. 1 9. 1. 2. 2. 1 , 3. 2. 1. 2. 0. 0. 0. 1. O [27]: N=len (data) [28]: N [28]: 1000 N is the number of events recorded We can easily compute the average with the following do loop [29]: ans=0 for i in range(1,N): ans ans+qdata[i-1] #do loop complete average=ans/N [30]: average [30]: 2.718 [ ]: Apply the simplest model of an infinite nearest neighbour queue with P1 = prob of jumping up and P2 = prob of jumping down. These can be estimated by counting the number of jumps up vs the number of jumps down. Consider the following do loop with if statements. [31]: nup=0 # nup counts no of up steps ndown=0 # ndown counts no of down steps for i in range(1,N): if qdata[i]>data[i-1]: nup=nup+1 elif qdata[i]data[i-1]: nup=nup+1 elif qdata[i]

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