MGSC 346: ch 4 Supplement B Waiting Lines

waiting time in line (using waiting line models to analyze operations)

long lines do not always mean long waiting times, depends on the service rate

mixed arrangement

most complex waiting line problem involves customers who have unique sequences of required services, therefore service can't be described neatly in phases (ex: medical center)

multiple channel, multiple phase arrangement

occurs when customers can be served by one of the fist phase facilities but then require service from a second phase facility and so on.

waiting line

one or more "customers" waiting for service

channel

one or more facilities required to perform a given service

impatient customer

one who either decides not to enter the system( balks) or leaves the system before being served (reneges)

Little's Law

relates # of customers in a a waiting line system to the arrival rate and waiting line of customers

priority rule

selects the next customer to be served by the service facility (determines which customer to serve next)

single server waiting line model

single server, single line of customers or single channel-single phase system

probability distributions

source of variation waiting line problems come from the random arrivals of customer sand the variations in service time

What does the exponential distribution assume?

that each service time is independent of those that preceded it and that service times can be very small and very large

number of customers in system (using waiting line models to analyze operations)

the # of customers in line and being served also relates to service efficiency and capacity

Line Length (using waiting line models to analyze operations)

the # of customers in the waiting line reflect one of two conditions. -Short lines: could mean either good customer service or too much capacity. -Long lines: low server efficiency or the need to increase capacity

service

the act of doing work for a customer

first come, first served rule FCFS- priority rule

the customer at the head of the line has the highest priority

Earliest promise due date EDD- priority rule

the customer with the earliest promise due date

What do the shapes in the service system mean?

they show diversity of customers with different needs

total time in system (using waiting line models to analyze operations)

total elapsed time from entry into the system until exit from the system may indicate problems with customers server efficiency, or capacity

multiple channel, single phase arrangement

used when demand is large enough to warrant providing the same service at more than 1 facility or when the service offered by the facilities are different

When is a Single Line service system best?

utilized at airline counters, inside banks, and at some fast food restaurants

When is a Multiple lines service system best?

utilized at grocery stores, drive in bank operations, and in discount stores

single channel, multiple phase arrangement

when services are best performed in sequence by more than 1 facility, yet customer volume or other constraints limit the design to 1 channel

infinite customer population

# of customers int he system does not affect the rate at which the population generates new customers

single server waiting line model assumptions

1. customers are patient; infinite population 2. arrivals follow a mean arrival rate: 1/lamdba 3. service time for one customer follows an exponential distribution with an average of 1/mu 4. waiting line priority rule is first come, first served

multiple server waiting line model assumptions

1. same as single-server, but with multiple, parallel servers 2. single line 3. when server finishes with customer, first person in line goes to the idle server 4. all servers are identical

preemptive discipline

a rule that allows a customer of higher priority to interrupt the service of another customer (ex: emergency rooms-patient with most life threatening injuries)

finite source waiting line model

a single server model missing one assumption bc here the customer population is finite, N potential customers have to be N >30

phase

a single step in providing the service

single channel, single phase arrangement

all services demanded by a customer can be performed by a single server facility (customers form a single line and go one at a time)

SimQuick

an easy to use package that is simply an Excel spreadsheet with some macros

customer population

an input that generates potential customers

interarrival times (arrival distribution)

another way to specify arrival distribution, it is the time between customer arrivals

service facility arrangements

are described by the # of channels and phases

waiting line models

are useful in capacity planning such as selecting an appropriate capacity cushion for a high customer contact process

What are the decision areas for management ?

arrival rates, number of service facilities, number of phases, number of servers per facility, server efficiency, priority rule, line arrangement

finite customer population

if the potential # of new customers for the service system is appreciably affected by the # of customers already in the system

service facility

consisting of a person or crew, a machine, or both necessarily to perform the service for the customer.

What is the structure of the waiting line problems description of the situation's basic elements?

customer population, a waiting line of customers, service facility, and priority rule (service system)

shortest expected processing time SPT- priority rule

customer with the shortest expected processing time

What is the assumption made about customers in the waiting line model?

customers are patient- one who enters the system and remains there until served.

arrival distribution

customers arrive at service facilities randomly (often described by a Poisson distribution)

multiple server waiting line model

customers form a single line and choose one of s servers when one is available

service system

describes the number of lines and the arrangement of the facilities

exponential distribution (for interarrival times)

describes the probability that the next customer will arrive, or that a service to a customer will conclude, in the next T time periods

Poisson Distribution

discrete distribution, the probabilities are for a specific # of arrivals per unit of time (involves mean and variance)

service time distribution--exponential distribution

exponential distribution describes the probability the the service time of the customer at a particular facility will be no more than T time periods