A queue with semiperiodic traffic

Juan Alvarez, Bruce Hajek

Research output: Contribution to journalArticlepeer-review


In this paper, we analyze the diffusion limit of a discrete-time queueing system with constant service rate and connections that randomly enter and depart from the system. Each connection generates periodic traffic while it is active, and a connection's lifetime has finite mean. This can model a time division multiple access system with constant bit-rate connections. The diffusion scaling retains semiperiodic behavior in the limit, allowing for both short-time analysis (within one frame) and long-time analysis (over multiple frames). Weak convergence of the cumulative arrival process and the stationary buffer-length distribution is proved. It is shown that the limit of the cumulative arrival process can be viewed as a discrete-time stationary-increment Gaussian process interpolated by Brownian bridges. We present bounds on the overflow probability of the limit queueing process as functions of the arrival rate and the connection lifetime distribution. Also, numerical and simulation results are presented for geometrically distributed connection lifetimes.

Original languageEnglish (US)
Pages (from-to)160-184
Number of pages25
JournalAdvances in Applied Probability
Issue number1
StatePublished - Mar 2005


  • Diffusion limit
  • Gaussian process
  • Overflow
  • Queueing
  • Semiperiodic traffic

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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