# Questions tagged [queuing-theory]

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### 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 ...
48 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 ...
104 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 $k$?
44 views

### 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 $2\mu$?
110 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 ...
18 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 ...
62 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 ...
36 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 ...
126 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 ...
348 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.
244 views

### 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{\...
82 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 ...