M／M

It looks like you've typed "M/M", which in many contexts refers to a class of queuing modelsin operations research and performance evaluation 鈥?specifically the M/M/c queue.

Here鈥檚 a brief explanation in case that's what you meant:

馃搱 M/M Queue Basics

The notation comes from Kendall鈥檚 notationfor queuing systems:

A / B / c

where:

• A= arrival process distribution
• B= service process distribution
• c= number of servers

Mstands for Markovianor Memoryless, meaning:

• Arrivals follow a Poisson process(exponential inter-arrival times).
• Service times are exponentially distributed.

So M/M/1is a single-server queue with Poisson arrivals and exponential service times.

M/M/cis the multi-server version.

馃搳 Key Properties of M/M/1

• Arrival rate: (\lambda)
• Service rate per server: (\mu)
• Traffic intensity: (\rho = \lambda / \mu) (must be (< 1) for stability in M/M/1)

Important formulas (steady state):

• Probability of (n) jobs in system:
  

  [

  P_n = (1 - \rho) \rho^n

  ]

• Average number in system:
  

  [

  L = \frac{rho}{1 - rho}

  ]

• Average time in system (Little鈥檚 Law):
  

  [

  W = \frac{1}{mu - lambda}

  ]

馃攣 Variants

• M/M/c鈥?c identical servers
• M/M/鈭?/strong>鈥?infinite servers (no queueing)
• M/M/c/K鈥?finite capacity K (at most K jobs in system)
• M/M/c/c鈥?loss system (Erlang-B, used in telephony)

If you meant something else by "M/M"鈥?for example:

• Male/Male(in fiction or romance genres)
• Manuscript formatting(M/M = manuscript markup)
• Mathematics(M/M = methods and materials)
• Or something else 鈥?/li>

Let me know and I can clarify further!