http://gljc.sxu.edu.cn/docs/2013-11/20131129080455222534.pdf

The discrete-time GI/Geo/1 queue with working vacations and vacation interruption

1. Explain why difference equations result from digital control of analog systems. 2. Obtain the z-transform of a given time sequence and the time sequence corresponding to a function of z. 3. Solve linear time-invariant (LTI) difference equations using the z-transform. 4. Obtain the z-transfer function of an LTI system. 5. Obtain the time response of an LTI system using its transfer function or impulse response sequence. 6. Obtain the modified z-transform for a sampled time function. 7. Select a suitable sampling period for a given LTI system based on its dynamics. Digital control involves systems whose control is updated at discrete time instants. Discrete-time models provide mathematical relations between the system variables at these time instants. In this chapter, we develop the mathematical properties of discrete-time models that are used throughout the remainder of the text. For most readers, this material provides a concise review of material covered in basic courses on control and system theory. However, the material is self-contained, and familiarity with discrete-time systems is not required. We begin with an example that illustrates how discrete-time models arise from analog systems under digital control.

Discrete-time systems

An M/G/1 queue with single working vacation and vacation interruption under Bernoulli schedule

https://ir.nctu.edu.tw:443/bitstream/11536/5405/1/000276790000018.pdf

Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation

The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation

The discrete time Geom/Geom/1 queue with multiple working vacations

We study a discrete-time Geom/Geom/c/c Erlang loss system. In this queueing system, we give the function equation that the generating function of the number of customers satisfies in steady-state system, and get the formula of stationary mean queue length. Furthermore, we derive recursive method to compute stationary queue length probability and loss probability. Finally, using a numerical example, we exemplify the relation between loss probability, the mean number of customers and various parameters

Performance Analysis of Discrete-Time Erlang Loss System

Abstract In this paper, an M/G/1 queue model with the multiple adaptive vacations and pure decrementing service policy is studied based on the classical M/G/1 queueing model. The PGF of stationary queue length is derived by using an embedded Markov chain method. The LST of stationary waiting time is also given according to the independence between waiting time and arrival process. The average probabilities of various system states are obtained. Some special cases are given to show the general properties of the new model.

Pure Decrementing Service M/G/1 Queue with Multiple Adaptive Vacations

We consider a Geom/G/1 gate service system with multiple adaptive vacation based on the classical Geom/G/1 queueing system. By using regeneration cycle approach, we obtain the PGF(Probability Generating Function) of the stationary queue length. Because of the independent property of the waiting time and the arrival process after its arrival, the PGF of the stationary waiting time is derived. Finally we obtain the average probabilities of various system state, some special cases are given to show the new model's general properties.

A geom/G/1 gate service system with multiple adaptive vacation

In this paper, an admission control scheme with priority for real-time traffic is designed, and a discrete time Geo1 +larr Geo2/Geo1,Geo2/s (preemptive priority) queue model is proposed to study the performance of the multi-traffic admission control scheme, which based on the running mechanism of the wireless multi-channel communication network and the various quality of service (QoS) requirement of multitraffic. Using matrix-geometric solution method, we get the performance measure, such as, average queue length for both traffic, blocking probability of real-time traffic and utilization rate of channel. And computer simulations verify the accuracy of the model

Mingxin Liu

Papers

The discrete time Geom/Geom/1 queue with multiple working vacations

Performance Analysis of Discrete-Time Erlang Loss System

Pure Decrementing Service M/G/1 Queue with Multiple Adaptive Vacations

A geom/G/1 gate service system with multiple adaptive vacation

Admission Control for Multi-Traffic in Wireless Multi-Channel Communication Network Based on Discrete Time Queue