This document discusses the application of queuing theory to library services. Queuing theory is the mathematical study of waiting lines and can help identify problems that occur when customers arrive randomly to receive services. In a library context, queuing theory can be applied to services like book circulation and counter services. A queuing model is represented by variables like arrival and service time distributions, number of servers, queue size and discipline. The objective is to determine the optimal service rate and number of servers to minimize average waiting time. Efficiency indices include traffic density, expected waiting time in queue, and expected number of customers in queue. An example is provided of modeling a library counter service with Poisson arrivals and exponential service times.
MCM,MCA,MSc, MMM, MPhil, PhD (Computer Applications)
Working as Associate Professor at Zeal Education Society, Pune for MCA Progrmme.
Having 18 Years teaching experience
MCM,MCA,MSc, MMM, MPhil, PhD (Computer Applications)
Working as Associate Professor at Zeal Education Society, Pune for MCA Progrmme.
Having 18 Years teaching experience
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Application of Queuing Theory to Libraries and Information Centres
1. Application of queuing theory to libraries and
information centres
By: Prajyot Naik.
IP-06
2. What is Queueing theory..?
• Queueing theory is the mathematical study of waiting
lines.
3. Problem identified by Queueing theory..?
• Queuing problem is identified by the presence of group of
customers who arrive randomly to receive some service.
• The customer, upon arrival may be attended to, immediately or
may have to wait until the server is free.
4. Scope of application in library
It is applicable to the following services provided in
the Library.
• circulation of books
• counter service
• allied services like reprography
5. Characteristics of a queuing model
A general queuing system is denoted by (a/b/c) : (d/e)
where
• a: probability distribution of inter arrival time
• b: probability distribution of service time
• c: number of counters in the system
• d: queue size
• e: queue discipline
6. Objective
• To find out the optimum service rate and the number of
servers (counters) so that, average cost of waiting in queuing
system is minimised .
7. Efficiency indices for queuing system are
• ρ = λ / μ = traffic density
• Wq = expected waiting time in queue
• Lq = expected number of customers in queue
• Where λ = mean arrival rate and μ = mean service rate.
8. Counter Service Example
• Suppose the service mechanism of the library has one
counter for issue/return of books.
• Let us assume the service time is exponential with
mean μ = 20 customers/hr.
• The arrival rate of customers (students as well as
faculty) at the counter be approximated by Poisson
distribution which is a satisfactory model in most
cases with arrival rate of one in 5 minutes
• It means average number of customers arriving is
12/hr .
