1. Queueing theory – Queuing theory is a branch of mathematics that studies how lines form,
how they function, and why they malfunction. Queuing theory examines every component
of waiting in line, including the arrival process, service process, number of servers, number
of system places, and the number of customers—which might be people, data packets,
cars, or anything else.
2. Queue - A queue is a line of people waiting for the moment a particular service or product
becomes available. In economic terms, it’s even simpler — a queue is a textbook case of
demands exceeding supply. When there are more people queuing up than there are clerks
ready to service them, we get queues.
3. Service cost – Service costing is the process of identifying all costs associated with
building, supporting, and delivering your service. Examples of service cost components
include equipment, staff labor, professional fees, software, license fees, and data center
charges, to name just a few.
4. Waiting cost – Waiting cost refers to the economic or non-economic costs incurred as a
result of waiting for a particular event, service, or product. It arises when individuals or
businesses have to spend time waiting for something instead of engaging in other
productive activities.
5. Finite calling population – In a finite population model, the arrival rate at a server is affected
by the population in the system. Usually the system is viewed as a closed system,
customers (with a fixed population) don't leave the system, they merely move around
system from one server to another, from one queue to another.
6. Infinite calling population – In an infinite population model, the arrival rate is not affected
by the number of customers in the system. Usually the system is viewed as an open
system, customers come from outside the system and leave the system after finishing the
work.
7. Poisson distribution – Poisson distribution is a probability distribution that is used to show
how many times an event is likely to occur over a specified period. In other words, it is a
count distribution. Poisson distributions are often used to understand independent events
that occur at a constant rate within a given interval of time.
8. Balking – Balking occurs when potential customers arriving at a queueing system choose
not to enter it.
9. Reneging – Reneging occurs when customers in a queueing system choose to leave the
system prior to receiving service.
10. Limited queue length – the length of the queue may be limited by the physical area in
which the queue forms; space may permit only a limited number of customers to enter the
queue.
11. Unlimited queue length – it is assumed that every person who comes joins the line. There
is no restriction on the number of people who are actually waiting or there is no restriction
on the length of the queue.
12. Queue discipline – Refers to the order in which members of the queue are selected for
service. Usually, first-come-first-serve is normally used.
13. FIFO – First In, First Out, commonly known as FIFO, is an asset-management and
valuation method in which assets produced or acquired first are sold, used, or disposed
of first. For tax purposes, FIFO assumes that assets with the oldest costs are included in
the income statement's cost of goods sold (COGS). The remaining inventory assets are
matched to the assets that are most recently purchased or produced.
14. Single channel system – Single channel refers to a producer or retailer’s effort to reach
customers through only one distribution option, regardless of whether it’s online,
catalogue, mail-order, face-to-face selling or traditional retail. This approach reduces
marketing investments and organizational complexity. However, the risk with this approach
is missed selling opportunities as customers shop alternative channels. This is particularly
risky, given how connected and empowered consumers are in the digital age.
15. Multiple channel system – Multi-channel refers to a producer or retailer’s effort to combine
and blend different distribution channels to accommodate where and how consumers
make purchases, ensuring that producers and retailers will be present when the purchase
decision is made. The objective is to make it easy for a consumer to buy in whatever way
is most appropriate for them. Multi-channel marketing allows the firm to reach its
prospective or current customers at the point of purchase in a channel of their liking. Most
firms with which you interact are engaged in multi-channel marketing, if not omni-channel
marketing.
16. Single phase system – the customers is served from only one server and then exits the
system.
17. Multiple phase system – the customer is served from several servers before exiting.
18. Negative exponential probability distribution – The negative exponential distribution is
used routinely as a survival distribution, describing the lifetime of a piece of equipment,
etc., put in service at what may be termed time zero. As such, it exhibits a lack of memory
property, which may not be desirable in this context.
19. Kendall notation – Kendall’s notation is used for parallel server systems. The basic format
of this notation is of form: A / B / c / N / K, where, A, B, c, N, K respectively indicate arrival
pattern, service pattern, number of servers, system capacity, and Calling population. The
symbols used for the probability distribution for inter arrival time, and service time are, D
for deterministic, M for exponential (or Markov) and Ek for Erlang.
20. Steady state – The steady state of a queuing system is the state where the probability of
the number of customers in the system is independent of time.
21. Transient state – The transient state of a queuing system is the state where the probability
of the number of customers in the system depends upon time.
22. Little’s flow equation – Little’s Law is a mathematical theorem in queueing theory that
determines the average number of items in a stationary queuing system. The Little’s Law
formula is frequently used in business development and project management systems
such as kanban (a popular visual system used to keep track of project activity) to improve
workflow and avoid bottlenecks. You can also use Little’s Law in any situation wherever
there’s a queue, whether it’s the number of people in line at the grocery store or tasks
executed by software.
23. Utilization factor – The utilization factor or use factor is the ratio of the time that a piece of
equipment is in use to the total time that it could be in use. It is often averaged over time
in the definition such that the ratio becomes the amount of energy used divided by the
maximum possible to be used.
24. Multichannel queuing system – Multichannel queuing systems mean when there is more
than one counter to serve the same service to a different customer.
25. Operating characteristics – The operating characteristic (OC) curve depicts the
discriminatory power of an acceptance sampling plan. The OC curve plots the probabilities
of accepting a lot versus the fraction defective. When the OC curve is plotted, the sampling
risks are obvious.
ANSWERS FROM CHATGPT:
1.
Queueing Theory: Queueing theory is a branch of mathematics that studies the
behavior and characteristics of waiting lines or queues. It provides mathematical
models and analysis techniques to understand and optimize the performance of
systems involving waiting lines, such as customer service centers, call centers,
transportation systems, and manufacturing processes.
2. Queue: A queue, in the context of queueing theory, refers to a waiting line where
entities (such as customers, jobs, or tasks) wait for service or processing. It
represents the sequence in which entities arrive and are served.
3. Service cost: Service cost refers to the cost associated with providing a service to
customers or processing entities in a queue. It includes expenses such as labor costs,
equipment costs, maintenance costs, and other operational expenses incurred to
deliver the service.
4. Waiting cost: Waiting cost, as explained earlier, refers to the economic or noneconomic costs incurred when individuals or businesses have to spend time waiting
for a particular event, service, or product. It encompasses the opportunity cost of the
time spent waiting and can also include subjective costs such as frustration or
dissatisfaction.
5. Finite calling population: In queueing theory, a finite calling population refers to a
situation where the number of potential entities (e.g., customers) that can join the
queue is limited and known in advance. The size of the population is predetermined
and does not change over time.
6. Infinite calling population: An infinite calling population, on the other hand, assumes
an unlimited number of potential entities that can join the queue. In this case, the
population size is so large that it is considered infinite for practical purposes.
7. Poisson distribution: The Poisson distribution is a probability distribution that is often
used to model the arrival rate of entities in a queueing system. It is characterized by
the assumption of events occurring randomly and independently over time, with a
constant average rate.
8. Balking: Balking refers to a behavior exhibited by entities in a queueing system, where
they choose not to enter the queue and decide to leave without receiving service.
Customers may balk if they perceive the waiting time or service conditions as
unfavorable.
9. Reneging: Reneging is another behavior observed in queueing systems, where
entities join the queue but leave before receiving service. Customers may renege if
they become impatient or if the waiting time exceeds their tolerance.
10. Limited queue length: A limited queue length implies that the queue has a maximum
capacity or a predefined limit on the number of entities it can accommodate. Once the
queue reaches its maximum capacity, incoming entities are denied entry or redirected
elsewhere.
11. Unlimited queue length: In contrast, an unlimited queue length means there is no
maximum capacity, and the queue can potentially accommodate an infinite number of
entities. This implies that no incoming entity is denied entry due to queue capacity
constraints.
12. Queue discipline: Queue discipline refers to the rules or algorithms used to determine
the order in which entities are served from the queue. It establishes the fairness and
orderliness of the queueing system.
13. FIFO: FIFO stands for "First-In, First-Out" and is a common queue discipline. In a FIFO
queue, the entity that arrives first is served first, and the order of service follows the
chronological order of arrival.
14. Single channel system: A single channel system refers to a queueing system that has
only one service facility or server available to process entities in the queue. The
entities are served one at a time.
15. Multiple channel system: A multiple channel system, also known as a multi-server
system, has more than one service facility or server available to process entities in
the queue. It allows simultaneous service of multiple entities, reducing overall
waiting times.
16. Single phase system: In a single phase system, entities require only one stage of
service or processing before they exit the queueing system.
17. Multiple phase system: A multiple phase system involves entities that require
multiple stages or phases of service or processing before they leave the queue. Each
phase represents a different step or activity in the overall service process.
18. Negative exponential probability distribution: The negative exponential probability
distribution is commonly used to model the inter-arrival times or service times in
queueing systems. It assumes that the probability of an event occurring within a given
time interval is exponentially distributed.
19. Kendall notation: Kendall notation is a standardized notation system used to describe
and represent queueing systems. It uses a three-part notation that includes symbols
for the arrival process, service process, and number of service facilities or servers.
20. Steady state: The steady state refers to the condition where the queueing system has
reached a stable equilibrium over time. In this state, the system's performance
measures, such as average waiting time and utilization, remain relatively constant.
21. Transient state: The transient state refers to the initial period when a queueing
system is not yet in a steady state. It represents the transitional phase where the
system's performance measures are changing as it approaches the steady state.
22. Little's flow equation: Little's flow equation, also known as the fundamental equation
of queueing theory, states that the long-term average number of entities in a
queueing system (L) is equal to the product of the average arrival rate (λ) and the
average time spent in the system (W).
23. Utilization factor: The utilization factor, also known as the traffic intensity or system
utilization, represents the ratio of the average service rate (μ) to the average arrival
rate (λ) in a queueing system. It indicates the level of resource utilization and can
help determine the system's performance.
24. Multichannel queuing system: A multichannel queuing system refers to a system that
has multiple service facilities or channels available for processing entities in the
queue. It allows for parallel processing of entities, reducing waiting times and
increasing system capacity.
25. Operating characteristics: Operating characteristics refer to the performance
measures used to evaluate the efficiency and effectiveness of a queueing system.
Common operating characteristics include average waiting time, average queue
length, system throughput, and resource utilization.