Question

In: Operations Management

Consider two systems: M/M/1 and M/M/1/k. There are two types of costs associated: (i) a rejection...

Consider two systems: M/M/1 and M/M/1/k. There are two types of costs associated: (i) a rejection cost r (cost per rejection); and (ii) a holding-cost rate h (cost per unit time per customer in system). Note that there is no rejection in M/M/1. Assuming ρ<1 for both systems, what is the condition for k that makes the M/M/1/k better than M/M/1. Simplify your answer as far as possible

Solutions

Expert Solution

Lets start with the basic.

QUEUEING MODELS -IS created to predict the the queue length & waiting time. queues are part of ones regular life and they are one of the most unpleasant experience of life .this mostly happens at the telephone exchange,supermarket,petrol station . queueing theory is the mathematical study of waiting lines & considered as branch of OPERATION RESEARCH ,with the help of it many business decisions are taken regarding providing sevices.QUEUEING THEORY is propounded in a research conducted by AGNER KRARUP ERLANG.

lets see the two theories

  1. M/M/1 -- this queue represent the queues length in a system having a single server .it is one of the basic models where their is only one server available to provide service to as many customer available.the model name is written in kendall's notation .where arrivals are determined by poisson process and job service by exponential distribution [i.e is the probability distribution that describes the time between events in a poisson point process.
  2. M/M/1/K-- here K represents the capacity of M/M/1 system ,that is the maximum number of customers in the system including the one under service this can easily get associated with the birth death process with rates .it should b noted that the system is stable for any p>0 when k is fixed .second condition is when K - INFINITE the stability condition will be p<1 ,since the distribution of M/M/1/K coverges to the distribution of M/M/1 .

Related Solutions

Consider the costs and benefits associated with various types of jobs with which you are familiar....
Consider the costs and benefits associated with various types of jobs with which you are familiar. Give examples of at least three: Describe the costs or risks associated with each job when voluntary turnover occurs. Identify the benefits which occur when someone voluntary leaves the job
Consider the group G = {1, −1, i, −i, j, −j, k, −k} under multiplication. Here...
Consider the group G = {1, −1, i, −i, j, −j, k, −k} under multiplication. Here i2= j2= k2= ijk = −1. determine which of the following sets is a subgroup of G. If a set is not a subgroup, give one reason why it is not. (a) {1, −1} (b) {i, −i, j, −j} (c) {1, −1, i, −i} (d) {1, i, −i, j}
Saalfrank Corporation is considering two alternatives that are code-named M and N. Costs associated with the...
Saalfrank Corporation is considering two alternatives that are code-named M and N. Costs associated with the alternatives are listed below: Alternative M Alternative N Supplies costs $ 82,000 $ 69,000 Assembly costs $ 50,000 $ 50,000 Power costs $ 30,000 $ 45,500 Inspection costs $ 43,000 $ 32,000 Required: a. Which costs are relevant and which are not relevant in the choice between these two alternatives? b. What is the differential cost between the two alternatives? a. Supplies costs Assembly...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k = 26, under the influence of an external force F(t) = 82 cos(4t). a) (8 points) Find the position u(t) of the mass at any time t, if u(0) = 6 and u 0 (0) = 0 . b) (4 points) Find the transient solution uc(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in...
Consider the following costs associated with pharmaceutical drug production. Which of the following are variable costs...
Consider the following costs associated with pharmaceutical drug production. Which of the following are variable costs and which are fixed costs? a) Research and development b) Manufacturing costs c) Market costs
Consider the following situation. a two-tailed test at the α = 0.1 Find the appropriate rejection...
Consider the following situation. a two-tailed test at the α = 0.1 Find the appropriate rejection regions. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) z>? z< ?
a) Consider an economy with two types of firms, S and I. Type S firms always...
a) Consider an economy with two types of firms, S and I. Type S firms always move together, but type I firms move independently of each other. For both types of firms, the expected return of an individual firm is given by 5%, and the return volatility of an individual firm is given by 25%. i) (10 points) There is an equally-weighted portfolio made of 10 type S firms and 10 type I firms. What is the expected return and...
What are the two primary types of Leveling I can consider in Microsoft Project to address...
What are the two primary types of Leveling I can consider in Microsoft Project to address resource constraints?
What are the types of costs associated with a project? What impact and relationship can you...
What are the types of costs associated with a project? What impact and relationship can you identify between these two variables and a project. Write at least two paragraphs to synthesize your ideas.
A technician compares repair costs for two types of microwave ovens (type I and type II)....
A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 54 type I ovens has a mean repair cost of $80.93. The population standard deviation for the repair of type I ovens is known to be $16.07. A sample of 35 type II ovens has a mean repair cost of $74.68....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT