1 Assume you have a system in which an entity is processed by two sequential servers. Eachserver has a capacity equal to 1. When the entity enters the system, the entity will beginprocessing with server 1 if server 1 is free. When the entity is finished processing with server1, it will move immediately to server 2. The entity will begin processing with server 2 if server2 is free. Both server 1 and 2 have an unlimited buffer capacities for entities to wait.Let T, be the simulation time of the nth state transition. The system state X(T) = (S(T).S2(T)) is the number of entities at server 1 and server 2. The states include entities who arebeing processed by a server. For example, if S,(T) = 1, then 1 entity is being processed and noentities are waiting. If S,(T) = 2. then 1 entity is being processed and 1 entity is waiting.The interarrival time for the entities follows an exponential distribution with a mean of 10minutes. The processing time of server 1 follows an exponential distribution with a mean of 7minutes.There is a stream of uniform random numbers for the interarrival times and server 1processing times: 0.33, 0.97The processing time of server 2 follows a uniform distribution between 4 and 14 minutes.There is a stream of uniform random numbers between 0 and 1 for server 2 processing tiuhes:0.44Assume X(Tn-1) = (2,0) and X(T) = (1,1). None of the uniform random numbers above havebeen used yet.What is the next event that will trigger the n+1st state transition?

The system consists of an entity that is processed by sequential servers. The capacity of each…

Assume you have a system in which an entity is processed by two sequential servers. Each server has a capacity equal to 1. When the entity enters the system, the entity will begin processing with server 1 if server 1 is free. When the entity is finished processing with server 1, it will move immediately to server 2. The entity will begin processing with server 2 if server 2 is free. Both server 1 and 2 have an unlimited buffer capacities for entities to wait. Let T be the simulation time of the nth state transition. The system state X(T) = (S₂(T). S2(T)) is the number of entities at server 1 and server 2. The states include entities who are being processed by a server. For example, if S₁(T) = 1, then 1 entity is being processed and no entities are waiting. If S₂(Tn) = 2. then 1 entity is being processed and 1 entity is waiting. The interarrival time for the entities follows an exponential distribution with a mean of 10 minutes. The processing time of server 1 follows an exponential distribution with a mean of 7 minutes. There is a stream of uniform random numbers for the interarrival times and server 1 processing times: 0.33, 0.97 The processing time of server 2 follows a uniform distribution between 4 and 14 minutes. There is a stream of uniform random numbers between 0 and 1 for server 2 processing times: 0.44 Assume X(Tn-1)=(2,0) and X(T) = (1,1). None of the uniform random numbers above have been used yet. What is the next event that will trigger the n+1st state transition?

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ