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M/M/c Queueing Network

Multi-server queue with arrivals, service, abandonment and overflow.

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digraph q {
  rankdir=LR;
  graph [bgcolor=transparent];
  node [shape=box, style="rounded,filled", fontname=Inter, fontsize=10];

  Arr [label="Arrivals\nλ (Poisson)", fillcolor="#dbeafe"];
  Q [label="Queue\n(FIFO)", fillcolor="#fef3c7"];
  S1 [label="Server 1\nμ", fillcolor="#dcfce7"];
  S2 [label="Server 2\nμ", fillcolor="#dcfce7"];
  S3 [label="Server c\nμ", fillcolor="#dcfce7"];
  Done [label="Departures"];
  Ab [label="Abandonment\n(impatience)", fillcolor="#fee2e2"];

  Arr -> Q;
  Q -> S1; Q -> S2; Q -> S3;
  S1 -> Done; S2 -> Done; S3 -> Done;
  Q -> Ab [style=dashed];
}