 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 rate  Randomness/Variability  Customers usually arrive at random intervals  Variability 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 wait › Customers leaving  Loss of customer goodwill.  Reduction in customer satisfaction.  Congestion may disrupt other business operations.

 To improve system Utilization  To minimize the sum of two costs › Customer waiting costs › Service capacity costs

1. An input, or customer population, that generates potential customers. 2. A waiting line of customers. (Customers Behavior) 3. 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. 4. A priority rule, which selects the next customer to be served by the service facility.

Customer population Service system Waiting line Priority rule Service facilities Served customers Figure C.1 – Basic Elements of Waiting-Line Models

Population Source Finite Infinite Example: 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 arrivals Customers from an infinite source do not affect the probability of another arrival

Customers are patient or impatient  Patient customers wait until served  Impatient 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 customer › No. of lines › No. of service channels › No. of service phases

Service Times ConstantVariable Example: Items coming down an automated assembly line. Example: People spending time shopping.

No. of lines in system › A 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 Service facilities (a) Single line Service facilities (b) Multiple lines

 Single-channel, single-phase  Single-channel, multiple-phase  Multiple-channel, single-phase  Multiple-channel, multiple-phase  Mixed arrangement

Service facility (a) Single channel, single phase (b) Single channel, multiple phase Service facility 1 Service facility 2 Examples of Service Facility Arrangements

(c) Multiple channel, single phase Service facility 1 Service facility 2 Service facility 3 Service facility 4 Service facility 1 Service facility 2 (d) Multiple channel, multiple phase

Routing for : 1–2–4 Routing for : 2–4–3 Routing for : 3–2–1–4 (e) Mixed arrangement Service facility 1 Service facility 4 Service facility 3 Service facility 2

Single Channel Multichannel Single PhaseMultiphase One-person barber shop/ ATM use Car wash Hospital admissions Bank tellers’ windows

 First-come, first-served (FCFS)—used by most service systems  Earlier 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.

 System Utilization  Average Number of Customers Waiting  Average Customer Time in System › Waiting time + processing time  Average Customer Waiting Time › Typically, you don’t want to keep the customer waiting for an unreasonable amount of time  Customer Waiting Costs  Service Costs  Probability of Lost Sales › Would like to minimize

1. Arrival rates 2. Line arrangement 3. Number of service facilities 4. Number of phases 5. Number of servers per facility 6. Server efficiency 7. Priority rule

 Reduce perceived waiting time › Tell customers how long their wait will be › Magazines in waiting rooms › Music/television › In-flight movies › Filling out forms  Derive benefits from waiting › Place impulse items in service facility › Advertise other goods/services › Encourage customers to come during the slack periods.