Aircraft systems
Classified in Computers
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Waiting line: use In manufacturing and service organizations to understand and arrive solutions To eliminate or minimize them.
Waiting lines tend to form if arrival and service patterns are highly variable because the Variability creates temporary imbalances of supply and demand.
Structure of waiting Line problems: An input, or customer population that generates potential Customers. A waiting line of Customers. The service facility, Consisting of a person (or crew), a machine (or group of machines), or both Necessary to perform the service for the customer. A priority rule, which selects the next customer to be served by The service facility
Customer population
The source of input: Finite or infinite source
Customers already in line from a finite source reduce the Chance of new arrivals
Customers already in line from an infinite source do not Affect the probability of another arrival
Customers are patient Or impatient: Patient customers wait until served
Impatient customers either balk (i.E. Do not enter the System) or renege (i.E. Leave the system before being served)
The service system:
Number of lines: Single, Multiple
Arrangement of Service facilities:
Single-channel, single-phase. Single-channel, multiple-phase. Multiple-channel, single-phase. Multiple-channel, multiple-phase. Mixed Arrangement
Priority rule: First-come, first-served (FCFS)—used by most service systems
Other rules:
Earliest due date (EDD)
Shortest processing time (SPT)
Preemptive discipline—allows A higher priority customer to interrupt the service of another customer or be Served ahead of another who would have been served first
Probability Distribution: The sources of variation in waiting-line problems come from The random arrivals of customers and the variation of service times
Arrival distribution: Customer arrivals can often be described by the Poisson distribution with Mean = T and variance also = T
Interarrival times are the average time between arrivals
Service time Distribution: Service time distribution can be described by an exponential Distribution with mean = 1/ and variance = (1/ )2
Single server model: Single-server, Single line of customers, and only one phase
Assumptions:
Customer population is infinite and patient
Customers arrive according to a Poisson distribution, with a Mean arrival rate of
Service distribution is exponential with a mean service rate Of
Mean service rate exceeds mean arrival rate
Customers are served FCFS
The length of the waiting line is unlimited
SINGLE SERVER MODEL FORMULA: Both the average waiting time in the system (W) and the average Time spent waiting in line (Wq) are expressed in hours. To convert the results To minutes, simply multiply by 60 minutes/ hour. For example, W = 0.20(60) = 12 Minutes, and Wq = 0.1714(60) = 10.28 minutes.
Multiple server model
Service system has Only one phase, multiple-channels
Assumptions (in Addition to single-server model)
There are s identical servers
The service distribution for each server is exponential
The mean service time is 1/
s should always exceed
Little’s law
Relates the number of customers in a waiting-line system to The arrival rate and the waiting time of customers
L = W or Lq = Wq
L = average number of customers in the system
= average arrival rate
W = average time a Customer spends in the system
Service; estimate W. Average time in facility = W= L customers/(A customer/hour)
Manufacturing: Estimate The average work-in-process L
Work-in-process = L = W