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
