2. A shopping center parking lot has ten spaces. Cars arrive at the...

  1. Home
  2. Homework Library
  3. Mathematics
  4. Probability
  5. 2. A shopping center parking lot has ten spaces. Cars arrive at the...


2. A shopping center parking lot has ten spaces. Cars arrive at the lot according to a Poisson process with rate λ > 0. If a car arrives at the lot and there is an empty space, it takes the space. If a car arrives and there are no empty spaces, the car moves on to another lot and never returns. Any parked car remains in its space for an exponentially distributed amount of time with mean 1/μ where M is a positive finite number. Assume that the times that different cars remain parked are independent and that these times are independent of the Poisson arrival process. Take as given that the number of cars in the lot at time t is a continuous time Markov chain.
(a) Determine the infinitesimal transition probabilities (that is the Q matrix) for this Markov chain. (It may be helpful to draw a diagram of the states with the infinitesimal rates marked on it).

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    50% discount

    $50.00 $25.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Probability Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats