Page 168 - ExtendSim User Guide
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142 Queueing
Queue/server systems
• TheActivityblockrepresentsservers:youcanspecifyanexponentialorotherdistributional service time within its dialog or by connecting a Random Number block (Value library) to its D (delay) connector.
M/M/1 queues
A standard notation often seen in queueing theory is M/M/1. This is a basic construct, repre- senting a single server queue. The notation translates to: exponential interarrival times/ expo- nential service times/ single server. It is also common to see the designation M/M/1/×, where the × translates to unlimited queue length, or the designation
M/M/1: ×/×/FIFO, which translates to exponential interarrival times/ exponential service times/ single server: unlimited queue length/ infinite population/ first in, first out service.
MM1 model
A typical M/M/1 system expressed using ExtendSim blocks, with the addition of a plotter and an Exit block, would look like the screenshot below.
MM1 model
Priority queues
As is true when any other sorting rule is used, a Queue block that sorts by priority will hold items until there is downstream capacity. Once the downstream block can accept an item, the Queue searches through the contents of the queue and releases the item with the highest prior- ity. For the Queue to work properly in this mode, items that enter should already have their pri- ority set; items without a priority are assigned a default Blank priority and get sent to the end of the waiting line.
Priority model
In the Priority exam-
ple, items enter the
model and immedi-
ately have their prior-
ity set to 2. They then
enter a Queue block
set to Sort by: priority.
After the machining
processes, each item is
inspected for flaws. If
the item does not pass
inspection, its priority
is re-set to 1 and it is sent back to the Queue block where it waits to be re-machined. When the machine can accept a new item, the Queue block will release the item with the highest priority. In this case, any item waiting to be re-machined will be released first.
Priority model
Discrete Event

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