Understanding the nature of traffic and its associated delay process in high traffic systems,rnsuch as the Internet, is essential for Engineering, Operations & Performance evaluation ofrnthese networks. It has been a common practice to assume packet arrivals as a Poisson Processrnin modelling high Traffic Networks. However, data communication traffic levels fluctuaternover time, and delays through congestion can occur even on lightly utilized links. Thesernfluctuations can occur over very short periods of time giving rise to the concept of a burst ofrntraffic. This high variability or bursty nature can be explained through Self-Similarity andrnLong-Range Dependence. In this thesis work an attempt is made to verify the Self-Similarityrnor Long-Range Dependence nature of Internet Traffic and its associated Packet Round TriprnDelay process. Also Fractional Auto-Regressive Integrated Moving Average (FARIMA)rnModel is found to fit the long memory as well as the short memory properties of the collectedrnInternet Traffic Data. An artificial traffic trace synthesis program based on the FARIMArnmodel is also developed.rnWhile the research convincingly establishes the presence of LRD over a wide range of timernscales in the packet traffic and delay processes, its implication to Queueing performance is arncenter of argument, in one hand arguments acknowledging LRD in packet traffic affectingrnQueueing performance, and in the other hand arguments emphasizing LRD has no practicalrnimpact and need not be incorporated into performance models. In this research it is tried to dornexperimentation, which demonstrates the first argument, that LRD in traffic indeed affectsrnQueueing Performance.rnTCP, the reliable transport protocol of TCP/IP, employs an ACK (acknowledgment)-basedrnwindow control, that is, a TCP sender updates its congestion window size every time itrnrandomly measures Round Trip Time (RTT) or Packet Round Trip Delay. With the mostrnbasic mechanism in the Internet to detect losses, the sender re-transmit a segment if it's ACKrnhas not been received in the expected amount of time. Therefore, TCP throughputrnperformance depends on the RTT. Investigation on the relation between RTT Self-Similarityrnand TCP throughput performance as measured by the amount of bandwidth wastage due tornpremature timeouts is also covered.rnvirnReal time traffic must get a fairly regulated number of packets through to the destination in arntimely manner. If these packets are late enough to have missed their â€œplayâ€ window, they arernuseless. Voice over Internet Protocol (VoIP) is one real-time application carried over thernInternet. Packet delay variations in Internet tend to create voice degradations, unless properrnQuality of Service (QoS) measures are implemented. In this thesis work investigation onrnPacket Delay and VoIP relations have been done and QoS measures suggested.