We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite buffer (M/G/1/n) systems. We show the somewhat surprising result that for three variations of the preemptive LCFS discipline, the maximum queue ...

A multiple optional vacation policy for the unreliable server batch arrival queueing system with essential and multi optional services under N-policy is investigated. According to vacation policy, the server takes an essential phase of vacation after the completion of service of an individual customer when queue becomes empty. On returning from the vacation, if the server finds the queue empty,...

This paper studies the performance of latency insensitive systems with limited queue size, in contrast with previous studies that assumed unlimited queue size. We obtain a tight theoretical performance upper bound of such systems. This paper also proposes an efficient implementation of latency insensitive systems. Experimental results show that our implementation can always reach the theoretica...

The so-called “Israeli queue” (Boxma et al. in Stoch Model 24(4):604– 625, 2008; Perel and Yechiali in Probab Eng Inf Sci, 2013; Perel and Yechiali in Stoch Model 29(3):353–379, 2013) is a multi-queue polling-type system with a single server. Service is given in batches, where the batch sizes are unlimited and the service time of a batch does not depend on its size. After completing service, th...

In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a parameter k defined as the system size of the finite approximation. The approximations capture the interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of the departures from an ME/ME/1 queue up to lag (k − 1).

We study the impact of service time distributions on the distribution ofthe maximum queue length during a busy period for the Mx/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come-first-served discipline,...

Router queues can impact both round-trip times and throughput. Yet little is publicly known about queue provisioning employed by Internet services providers for the routers that control the access links to home computers. This paper proposes QFind, a black-box measurement technique, as a simple method to approximate the size of the access queue at last mile router. We evaluate QFind through sim...

Random Early Detection (RED) has been introduced as a congestion avoidance algorithm for the Internet. RED detects congestion by estimating the average queue size. It drops packets probabilistically before buuer overrow, with the drop probability depending on the average queue size. In this paper, we analyse the innuence of RED on the packet loss ratio and the throughput of a system consisting ...

In this paper we analyze the performance of 802.15.4 Wireless Sensor Network (WSN) and derive the queue size trade off for different modulation schemes like: Minimum Shift Keying (MSK), Quadrature Amplitude Modulation of 64 bits (QAM_64) and Binary Phase Shift Keying (BPSK) at the radio transmitter of different types of devices in IEEE 802.15.4 for WSN. It is concluded that if queue size at the...

This paper studies the Ethernet Passive Optical Network (EPON) with gated-limited service. The transmission window (TW) is limited in this system to guaranteeing a bounded delay experienced by disciplined users, and to constrain malicious users from monopolizing the transmission channel. Thus, selecting an appropriate TW size is critical to the performance of EPON with gated-limited service dis...