# Aircraft systems

Classified in Computers

Written at on English with a size of 4.5 KB.

**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