This study uses an approximate Markov chain to determine that the sliding window (SW) parallel packet switch (PPS) runs only slower than the external line speed in order to simulate first-in-first-out (FCFS) output queueing (OQ) data Packet switching. In a previous study by the author [1], a new PPS SW packet switching scheme was proposed, called SW-PPS. The PPS class is characterized by the deployment of a distributed central-level switching plane, and its memory buffer runs slower than the external line speed. Given identical Bernoulli and Bursty data traffic, the proposed SW-PPS provides significantly better performance than typical PPS. In typical PPS, the scheduling algorithm uses the round-robin method (RR) [1]. This research developed a proposed Markov chain model that successfully demonstrated throughput, cell delay, and cell loss rate. Simulations show that the chain is accurate for a reasonable network load. Major findings about the proposed model are: (1) SW-PPS throughput and cell drop rate can theoretically simulate FCFS-OQ packets when each slower packet switch is running at a rate of approximately R / K Switch throughput and cell drop rate. (Eq. 19); and, (2) The study also proved the theoretical pos-sibility that the cell delay of a SW-PPS can emulate that of an FCFS-OQ packet switch, when each slower packet switch operates at a rate of about (R/cell delay of FCFS-OQ switch) (Eq. 20).