OPM Supplement B
Waiting Line = one or more “customers” waiting for service
- Waiting lines form due to a temporary imbalance between the demand for
service and the capacity of the system
Structure of waiting line problems:
1. An input, or customers population, that generates potential customers
2. A waiting line of customers
3. The service facility, consisting of a person (or crew), a machine (or group
machines), or both necessary to perform the service for the customer
4. A priority rule, which selects the next customer to be served by the service
facility
Numer of lines:
- Single (1 kassa, 1 rij)
- Multiple (meerdere kassa’s, meerdere
rijen)
Arrangements of service facilties:
- Channels
- Phases
Figuur 1single channel, single phase Single channel, multiple phase Multiple channel, single phase
Priority Rules:
- First come, first-served (FCFS)
- Earliest due date (EDD)
, - Shortest processing time (SPT)
- Preemptive discipline = a rule that allows a customer of higher priority to
interrupt the service of another customer
Probability Distributions:
- Arrival distribution
Pn = Probability of n arrivals in T time periods
λ = Average numbers of customer arrivals per period
e = 2.7183
- Remark: e = Euler’s number, a mathematical constant that is the base of the
natural logarithm. It is approximately equal to 2.71828 and is the limit of (1 +
1/n)n as n approaches infinity. It can also be calculated as the sum of the
infinite series
- Service time distribution
μ = average number of customers completing service per period
t = service time of the customer
T = target service time
Using waiting line models to analyze operations:
- Balance gains that might be made by increasing the efficiency of the service
systems against the costs of doing so
- Operating charactistics
o Line length
o Number of customers in system
o Waiting time in line
o Total time in system
o Service facility utilization
Single server model:
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lieker. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.27. You're not tied to anything after your purchase.