# Questions tagged [queuing-theory]

Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.

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### Elevator Traffic (Queueing Theory) Papers

I am about to start my final year thesis. The topic would be related to the queueing theory, specifically for the elevator traffic systems. I would need to do some literature review before going ...
462 views

### Significant bias introduced into simple simulation

This question has been asked on Cross Validated Introduction Service is allocated to an infinite source of customers i.e. there is always a service in progress. The duration of the $i^{th}$ service ...
58 views

### Minimising average holding cost per unit time is equivalent to minimising average delay per customer in queue

This question was originally asked on Math Stack Exchange. It is probably better suited here. Introduction When one thinks about a queue, it is natural to want to find a policy that minimises the ...
20 views

### What are some references for Fluid and Diffusion models in Queuing?

In queuing theory and stochastic process, there are many papers that have applied fluid and diffusion models to approximate the original models. However, the concepts and basics of these models are ...
51 views

### How would I model the following problem concerning customer service via FCFS vs Appointment Scheduling

I'm unfamiliar with OR, and would like to get some advice on how to "think" about this scenario: I work for an organization that primarily has store fronts. Customer's arrive throughout the ...
42 views

### Clearing a backlog(queue) of emails

I have this theoretical problem that I want to solve. Let's say there is a a bank that went bankrupt. Luckily they can still pay back all their customers, the only thing they have to do is to send an ...
63 views

### Service probability for M/M/1 queue with reneging

Consider an M/M/1 queue with arrival rate $\lambda$ and service rate $\mu$, where participants renege after a random amount of time which follows an exponential distribution with mean $\tau$. We ...
439 views

### How do derive the steady state probabilities M/M/1/k queueing system?

How do I derive the steady state probabilities for the $M/M/1/k$ queueing systems with finite system capacity $k$?
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### Two M/M/1 queues working independently

If two M/M/1 queues with arrival rate $\lambda$ and service rate $\mu$ are working independently. Is the system equivalent to a single M/M/1 queue with arrival rate $2\lambda$ and service rate $2\mu$?
122 views

### Waiting time in M/M/n queue

I was able to numerically "show" that an M/M/n queue is concave increasing in the number for $n$ servers, which makes intuitive sense. However is there a formal analytical proof for it? Where can I ...
24 views

### Approximate average waiting time when a m\m\1 queue shows transient behavior

I have an m/m/1 queue and a set of arrival rate $\{\lambda_{t_1}, \lambda_{t_2} ...., \lambda_{t_n}\}$ and a fixed service rate $\mu$. I want to calculate the average waiting time during each time ...
66 views

### Combining Two Different Queues

I am trying to create an optimization model for a problem that involves two different types of queues. Given Poisson demand (for both), there is a queue with constant service time and another queue ...
79 views

### MPX Queuing Software for Manufacturing with the GTHUBS Case

I'm teaching an Operations Management Class. A long time ago, there was a simple DOS-based product called MPX. It was based on queuing theory and let you model manufacturing processes. There was ...
151 views

### Queuing Theory with Learning Perspective

I am willing to work on queuing models but in classical queuing models, it is assumed the probability distributions of arrival and service are known or at least the rate is known. However, I am ...
360 views

### Current Issues of Interest

What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.
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### Convexity/Concavity of Average Number of Jobs in M/M/1 Queue?

I am working on a problem involving the average number of jobs $L$ in an M/M/1 queue with arrival rate $\lambda$, service rate $\mu$. For traffic intensity $\rho = \frac{\lambda}{\mu}$,  L = \frac{\...
86 views

### Queuing Theoretic Model with Memory

Consider a telephone company which receives call request at some arrival rate and serves each request with some service rate. This can be modeled using a Poisson Process. However I wish to model the ...