Queuing Theory Problem

I am submitting a couple of queuing theory problems that I was trying to solve for practice and study. I'm having trouble getting them formulated. --- Queuing Theory Question 1 An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane. If 2 swimmers are in a lane, each swims up and down one side of the lane. Swimmers always join the lane with the fewest number of swimmers. If all 3 lanes are occupied by 2 swimmers, a prospective swimmer become... click for more

Linear Problems using excel or lindo

I need assistance in developing the restraint equations for the attached problem. I have tried developing them and creating the linear equations to input into Lindo and am continuously getting error messages and I am not sure what it is I am doing wrong. Thank you. (See attached file for full problem description) --- Sunco Oil Co. manufactures three types of gasoline: Gas 1, Gas 2 and Gas 3. Each type is produced by blending three type of crude oil: Crude 1, Crude 2 and Crude 3. The sales price per barrel of gasoline and the purchase price per barrel of crude oil is given in the following table: Gasoline Type Gas Selling Price Per Barrel Crude Oil Type Crude Oil Purchase Price Per... click for more

Dantzig-Wolfe / Bender decomposition in LP

This is PhD level LP question. Of course it does not mean that only PhD people can solve it. What I'd like to ask is please give me a guide how to solve this problem by using Dantzig-wolfe and Bender decomposition. It won't be hard, but I'd like to check if I'm on a right track. (See attached file for full problem description)

Prove this by using duality, Farkas lemma

this question is from linear programming. I want to use duality (it's so obvious), farkas lemma (alternative solution) and all. (See attached file for full problem description with equations) --- (a) Let . Prove that one of the following systems has a solution but not both: (b) Prove or disprove the following claim: Assume that both the linear program min s.t. and its dual max s.t. are feasible. Then at least one of them has an unbounded feasible region. ---

Exam Review for Stochastic Processes part 5

(See attached file for full problem description) --- Consider the M/M/s queue, with arrival rate... ---