In this work, we consider the performance analysis of state dependent priority traffic and scheduling in device to device (D2D) heterogeneous networks. There are two priority transmission types of data in wireless communication, such as video or telephone, which always meet the requirements of high priority (HP) data transmission first. If there is a large amount of low priority (LP) data, there will be a large amount of LP data that cannot be sent. This situation will cause excessive delay of LP data and packet dropping probability. In order to solve this problem, the data transmission process of high priority queue and low priority queue is studied. Considering the priority jump strategy to the priority queuing model, the queuing process with two priority data is modeled as a twodimensional Markov chain. A state dependent priority jump queuing strategy is proposed, which can improve the discarding performance of low priority data. The quasi birth and death process method (QBD) and fixed point iteration method are used to solve the causality, and the steadystate probability distribution is further obtained.Then, performance parameters such as average queue length, average throughput, average delay and packet dropping probability for both high and low priority data can be expressed. The simulation results verify the correctness of the theoretical derivation. Meanwhile, the proposed priority jump queuing strategy can significantly improve the drop performance of lowpriority data.
Devicetodevice (D2D) communication is a modern communication method that allows direct communication between nearby users, which is considered to be one of the key technologies of 5G communication system [
In [
Existing works have applied the priority jump queue model to wireless packet networks or cognitive radio networks [
So far, few papers have applied the priority queue model to the D2D cellular heterogeneous network. Reference [
This paper focuses on the multiclass service transmission model in the D2D underlying cellular network. Combined with queuing theory and Stochastic geometry, a spatiotemporal model is proposed to analyze the performance of cellular users in heterogeneous networks. First, we consider the transmission mode of potential D2D users in the cellular network which adopts a distancebased D2D mode selection strategy. At the same time, considering that the interference is caused by users who use nonempty buffers, we use the thinning Poisson point process to model the spatial distribution of cellular users and obtain the probability of successful transmission. Second, we consider the priority transmission status of multiple business models, which can make full use of the buffer space. The priority jump strategy with a common buffer area in the queuing theory is adopted to provide more transmission opportunities for lowpriority data, thereby alleviating the starvation state of lowpriority data under high load. A twodimensional Geo/G/1 Markov chain is established to describe the queue model with priority switching strategy for each cellular user, and the quasibirth and death (QBD) method is used to evaluate the queuing behavior. When calculating the steadystate probability distribution, the iterative solution is used to calculate the steadystate probability distribution and obtain the expression of performance indicators.
The rest of this paper is organized as follows. The Section 2 describes the system model and performance indicators. The queuing model analysis framework with priority jumping is established in the Section 3. Queue stability analysis and performance parameters are introduced in Section 4. Section 5 provides numerical and simulation results, followed by the conclusions of Section 6.
As shown in
This paper considers that the uplink spectrum resources in the cell are orthogonally allocated to different cellular users. Potential D2D users reuse the channel in an underlay manner. It is assumed that the cellular network is in a fully loaded state, that is, all uplink subchannels in the cell are allocated to different cellular users. We adopt a mode selection strategy for potential D2D users. When the distance between the D2D transmitter and the target receiver is less than the preset threshold, the potential D2D user will work in D2D mode, that is, sharing channel resources with cellular users for direct communication. At this time, D2D communication will cause interference to the cellular link of the shared channel. When the distance between the D2D transmitter and the receiver exceeds the threshold, the D2D user enters the sleep mode [
We assume that each potential D2D receiver is randomly distributed around its potential transmitter, and the distance from the transmitter to the receiver
We consider the path loss plus block fading channel model [
Additionally, as we consider the uplink transmission, power control is necessary. Uplink power control is used to adjust the transmit power to keep the base station receiving the signal power from the cellular user at a certain value, we employ the full channel inversion for uplink power control [
According to the above assumptions, cellular users
Considering the interference limited system, we can get the expression of the signal to interference and noise ratio of cellular user
In this section, we build a dynamic priority queuing model with a common buffer area, and discuss statedependent priority jump strategies.
We use the twodimensional Geo/G/1 Markov chain to establish a priority queue model for cellular users, where Geo represents the arrival process that obeys the geometric distribution, and G represents the service time, which is a nonnegative random variable. Taking into account the actual interference received by cellular users in the D2D underlying cellular network, the service process is determined by the SINR value of each time slot. For the convenience of analysis, this paper takes two types of priority data as examples. For the case of multiple types of priority, the derivation process is similar. By setting the jumping probability
(1) Data packet arrival process
It is assumed that the data packets arrival of the cellular user obeys the Bernoulli distribution with the parameter
(2) Service process
Assuming that the cellular user is sending at the maximum rate, the sending rate is
The complementary cumulative distribution function (CCDF) of the cellular link SINR can be expressed as
Formula
The derivation of
In this discretetime queuing system, we assume that each cellular user can only send one data packet in one time slot. In the transmission process of multiple data types, services such as video or telephony, which require high delay, need to be transmitted first and set as HP data. Data services like short messages have lower latency requirements and are set as LP services. The priority queuing model used in this paper always meets the transmission of HP data first. If there is a large amount of LP data, there will be a large amount of LP data that cannot be sent. This situation will lead to excessive delay and packet loss of LP data. We consider adding a priority jump strategy to the priority queuing model to allow low priority data packets to be sent as high priority data with a certain jump probability. The jump probability is determined by the number of data packets in the high and low priority queues. it is called state dependent priority jump strategy.
As shown in
First, as long as there is high priority data in the queue, high priority data will be sent first, and LP data will be sent when the HP buffer is empty. Secondly, if there is only high priority data in the queue and the queue is not full, the packets will enter the queue with probability 1 and to be transmitted. If the queue is full, the arriving HP data will be discarded with probability 1. Third, when the number of data packets in the buffer of the HP queue is
In this queuing system, we consider a Statedependentbased priority jump strategy as follow
In order to analyze the transmission behavior of high and low priority data under the jump strategy respectively, we regard the two types of data entering the same buffer as two virtual queues. We use a twodimensional Markov chain to model the data transmission of cellular user. The system state can be represented by the number of data packets
The transition probability matrix
The high priority queue length is 0, and the phase (LP queue length) plus 1 or minus 1, expressed as:
For
For the boundary conditions
The submatrix
For
For boundary conditions of
The submatrix
The steadystate solution of the quasibirthdeath process can be obtained by solving the linear balance equations, which is the column matrix of steadystate probability. In order to use the regular structure of the block matrix, we will divide the quasibirthdeath process into:
From the linear balance equation, in order to solve the steadystate probability
After the steadystate probability distribution is obtained by Algorithm 1, performance parameters such as average queue length, average throughput, average delay and packet dropping probability can be expressed as the following expressions. The expressions of the average captain of HP and LP are given as:
Given the steadystate probability distribution and the probability of successful transmission, the average throughput of HP and LP queues can be derived as:
In addition, Little’s law can be used to evaluate the average waiting time
Furthermore, we can give the closedform expressions of the packet dropping probability as:
In this section, we use MATLAB to analyze and verify the correctness of the mathematical expressions of the above performance parameters, and explore the system performance by changing the parameters in
Density of D2D user pairs ( 


Density of BS ( 

Data packet size ( 
100 
Time slot duration ( 
1 
Transmit power of D2D ( 
20 
Additive white gaussian noise power  −104 
D2DTX to D2DRX transmission distance ( 
25 
Buffer capacity ( 
50 packets 
The receiver sensitivity of BS ( 
−80 
The path loss factor of D2D link ( 

The path loss factor of CU link ( 
3.5 
A spatiotemporal mathematical model in the D2D underlying cellular network was proposed. Different from the existing results, we focus on the multipriority business mode. Stochastic geometry and priority queuing theory are adapted in this network. We set a priority jump strategy to provide transmission opportunities for LP data and reduce the packet dropping probability of the LP queue. In addition, considering the transmission mode of potential D2D users in the cellular network, we adopt a distancebased D2D mode selection scheme. To show the relationship between the D2D user queues, we model the positions of D2D users with Nonempty queue buffers using a thinned Poisson point process to derive the CCDF of the D2D receiving SINR. Secondly, we use a twodimensional Geo/G/1 Markov chain to describe the queue model with priority jumps for D2D users, and the QBD method evaluates the queue state transition process. Finally, a series of expressions of performance parameters are derived, such as average queue length, average throughput, average delay and packet dropping probability. Simulation analysis confirmed the correctness of the numerical analysis. In addition, by comparing the packet loss rate of priority queues with and without jump strategy, the rationality of the model proposed in this paper is explained. In future work, we can apply the queuing model and analytical approach presented in this paper to conducting performance studies on D2Dassisted wireless caching networks. Specially, we can discuss the service transmission model of D2D heterogeneous cellular network in full duplex mode, and further analyze various types of jump strategies. We can also consider D2D equipment powered by precharged batteries from the perspective of green communication.The harvested energy can signifificantly improve the lifetime of the device and the network. we will concentrate on using more realistic assumptions to build a dynamic model in further research. We hope our work can provide a more accurate theoretical basis for the design of the actual system.
Guangjun Liang and Jianfang Xin conceived and designed the experiments; Guangjun Liang and Lingling Xia performed the experiments; Xueli Ni and Yi Cao analyzed the data; Guangjun Liang wrote the paper. All authors have read and agreed to the published version of the manuscript.