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We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL) in discrete time, which complements the sample-path and stationary versions of the PLL we recently established, motivated by data analysis of a hospital emergency department. Our new CLT version of the PLL extends previous CLT versions of LL. As with the LL, the CLT version of the PLL is useful for statistical applications.more » « less
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We develop a general framework for stationary marked point processes in discrete time. We start with a careful analysis of the sample paths. Our initial representation is a sequence {(tj,kj) :j∈Z} of times tj∈Z and marks kj∈K, with batch arrivals (i.e.,tj=tj+1) allowed. We also define alternative interarrival time and sequence representations and show that the three different representations are topologically equivalent. Then, we develop discrete analogs of the familiar stationary stochastic constructs in continuous time: time-stationary and point-stationary random marked point processes, Palm distributions, inversion formulas and Campbell’s theorem with an application to the derivation of a periodic-stationary Little’s law. Along the way,we provide examples to illustrate interesting features of the discrete-time theory.more » « less
