Page 225 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Another element of queuing system is service system. The number of waiting lines, the number
of servers, the arrangements of the servers, the arrival and service patterns, and the service
priority rules characterize the service system. Queue system can have channels or multiple
waiting lines.

Example: Single waiting line : bank counter, airline counters, restaurants, amusement
parks.

In these examples multiple servers might serve customers. In the single line multiple servers
has better performance in terms of waiting times and eliminates jockeying behavior than the
system with a single line for each server. System serving capacity is a function of the number of
service facilities and server proficiency. In waiting line system, the terms server and channel are
used interchangeably. Waiting line systems are either single server or multiple servers.

Example:
1. Single server: gas station, food mart with single checkout counter, a theater with a
single person selling tickets and controlling admission into the show.

2. Multiple server: gas stations with multiple gas pumps, grocery stores with multiple
cashiers, multiple tellers in a bank.
Services require a single activity or services of activities called phases. In a single-phase system,
the service is completed all at once, such as a bank transaction or grocery store checkout counter.
In a multiphase system, the service is completed in a series of phases, such as at fast-food
restaurant with ordering, pay, and pick-up windows.
The process of waiting line is characterized by rate at which customers arrive and are served by
service system. Arrival rate specifies the average number of customers per time period. The
service rate specifies the average number customers that can be serviced during a time period.
The service rate governs capacity of the service system. It is the fluctuation in arrival and service
patterns that causes wait in queuing system. A general waiting line system with parallel server
is shown in Figure 8.1.
Self Assessment

Fill in the blanks:
4. A bank transaction or grocery store checkout counter is an example of ……………..system.
5. ……………… specifies the average number of customers per time period.
6. The ………………… governs capacity of the service system.

7. It is the fluctuation in ……………… and …………..patterns that causes wait in queuing
system.
8. When customer changes one line to another to reduce wait time, process is called
…………………….

11.3 Poisson and Exponential Distributions

Both the Poisson and Exponential distributions play a prominent role in queuing theory.
Considering a problem of determining the probability of n arrivals being observed during a
time interval of length t, where the following assumptions are made.

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