One or more customers waiting for a service.Customer can be:People e.g. A person waiting in line to deposit cash in a bank.Objects e.g. A machine waiting for maintenance, Inventory waiting to be delivered. Truck waiting to be loaded etc.See Page # 291 (Book-1)

Temporary imbalance between demand and capacity.Larger arrival rate than servicing rateRandomness/VariabilityCustomers usually arrive at random intervalsVariability in order lengths some orders take longer than others

Waiting lines are non-value added occurrences.Waiting in lines does not add enjoyment for customers.Waiting in lines does not generate revenue for company.Costly to provide additional waiting space.Possible loss of business.Customers refusing to waitCustomers leavingLoss of customer goodwill.Reduction in customer satisfaction.Congestion may disrupt other business operations.

To improve system Utilization

To minimize the sum of two costsCustomer waiting costsService capacity costs

An input, or customer population, that generates potential customers.

A waiting line of customers. (Customers Behavior)

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.

Figure C.1 Basic Elements of Waiting-Line Models

Population SourceExample: Number of machines needing repair when a company only has three machines.Example: The number of people who could wait in a line for gasoline. Customers from a finite source reduce the chance of new arrivalsCustomers from an infinite source do not affect the probability of another arrival

Customers are patient or impatient

Patient customers wait until servedImpatient customer behave in different ways:Balking: When customer decides not to enter in line.Jockeying: When customer switches to another line.Reneging: When customer quits waiting and leaves the line.

Service rate depends on the structure of service system and facility.Structure of a service system depends on various factors such as:

Service time for customerNo. of linesNo. of service channelsNo. of service phases

Service time for customerServiceTimesExample: Items coming down an automated assembly line. Example: People spending time shopping.

No. of lines in systemA single-line keeps servers uniformly busy and levels waiting times among customers A multiple-line arrangement is favored when servers provide a limited set of services

Single-channel, single-phaseSingle-channel, multiple-phaseMultiple-channel, single-phaseMultiple-channel, multiple-phaseMixed arrangement

(a) Single channel, single phase(b) Single channel, multiple phaseExamples of Service Facility Arrangements

(c) Multiple channel, single phase(d) Multiple channel, multiple phase

(e) Mixed arrangement

Single ChannelMultichannelSingle PhaseMultiphase

First-come, first-served (FCFS)used by most service systemsEarlier Due Date (EDD)Shortest Processing Time (SPT)Preemptive disciplineallows a higher priority customer to interrupt the service of another customer or be served ahead of another.

System UtilizationAverage Number of Customers WaitingAverage Customer Time in SystemWaiting time + processing timeAverage Customer Waiting TimeTypically, you dont want to keep the customer waiting for an unreasonable amount of timeCustomer Waiting CostsService CostsProbability of Lost SalesWould like to minimize

Arrival ratesLine arrangement Number of service facilitiesNumber of phasesNumber of servers per facilityServer efficiencyPriority rule

Reduce perceived waiting timeTell customers how long their wait will beMagazines in waiting roomsMusic/televisionIn-flight moviesFilling out formsDerive benefits from waitingPlace impulse items in service facilityAdvertise other goods/servicesEncourage customers to come during the slack periods.