Page 18 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

thors consider a system with an Age‑of‑Information (AoI) nel. The authors provide a delay‑MaxWeight scheduler
oriented user and a deadline‑constrained user. The au‑ that has proven its throughput is optimal. Research on
thors provide the distribution of the AoI and the packet scheduling heterogeneous traf ic with Ultra‑Reliable Low
drop rate and they examine the interplay between them. Latency (URLLC) users and enhanced Mobile Brodband
Furthermore, energy and power ef icient scheduling (eMBB) has attracted a lot of attention by the com‑
schemes for delay‑constrained traf ic have attracted a lot munity [26]‑ [33]. In [26], [27], the authors show the
of attention over the last the few years [11–16]. In [11], bene its of lexible Transmission Time Interval (TTI) for
the authors consider the minimization of drop rate for scheduling users with different types of requirements.
users with a limited power‑budget. They propose an In [28], the authors propose an algorithm that jointly
approximated algorithm that performs in real time. In schedules URLLC and eMBB traf ic. They consider a
[12], the authors propose an algorithm that minimizes slotted time system in which the slots are divided into
the time average power consumption while guaranteeing mini slots. They consider the frequency and mini‑slots
minimum throughput and reducing the queueing delay. allocation over one slot. In [29], the authors consider the
They also consider a hybrid multiple access system where resource allocation for URLLC users. They study resource
the scheduler decides if the transmitter serves a user by allocation for different scenarios: i) OFDMA system,
orthogonal multiple access or non‑orthogonal multiple ii) system that includes retransmissions. In [30], [31],
access. In [13], [14], the authors utilize Markov decision the authors propose a low‑complexity algorithm for
theory to provide an optimal energy‑ef icient algorithm scheduling URLLC users. The authors in [32] consider
for delay‑constrained users. the throughput maximization and HARQ optimization for
Lyapunov optimization theory has been widely applied URLLC users. Furthermore, reliable transmission is an
for developing dynamic algorithms that schedule users important issue of URLLC communications. In [33], the
with packets with deadlines. In [17–20], the authors con‑ authors consider a network in which multiple unreliable
sider the rate maximization under power and delay con‑ transmissions are combined to achieve reliable latency.
straints. In [17], the authors consider the power alloca‑ The authors model the problem as a constrained Markov
tion for users with hard‑deadline constraints. In [18], the decision problem, and they provide the optimal policy
authors consider the rate maximization of non‑real‑time that is based on dynamic programming.
users while satisfying the packet drop rate for users with
packets with deadlines. In [19,20], consider packets with 1.2 Contributions
deadlines for scheduling real‑time traf ic in wireless en‑
vironments. A novel approach for minimizing the packet In this work, we consider two sets of users with hetero‑
drop rate while guaranteeing stability is provided in [21]. geneous traf ic and a limited‑power budget. The irst
The authors combine tools from Lyapunov optimization set includes users with packets with deadlines and the
theory and Markov decision processes in order to develop second set includes users with minimum‑throughput re‑
an optimal algorithm for minimizing the drop rate under quirements. We provide a dynamic algorithm that sched‑
stability constraints. However, the algorithm is able to ules the users in real time and minimizes the drop rate
while guaranteeing minimum throughput and limited‑
solve small network scenarios because of the curse of di‑
power consumption. The contributions of this work are
mensionality problem.
Besides delay‑constrained traf ic management, the following.
throughput‑optimal algorithms have been developed • We formulate an optimization problem for minimiz‑
over the years. Following the seminal work in [22], ing the drop rate with minimum‑throughput con‑
many researchers developed different solutions for straints and time average power consumption con‑
the throughput‑maximization problem by proposing straints.
a variety of approaches [23–25]. In [23], the authors
consider the throughput‑maximization while guaran‑ • We provide a novel objective function for minimizing
teeing certain interservice times for all the links. They the drop rate. The objective function does not take
propose the time‑since‑last‑service metric. They com‑ into account only if a packet is going to expire or not,
bine the last with the queue length of each user and but also the remaining time of a packet before its ex‑
they propose a max‑weight policy based on Lyapunov piration.
optimization. In [24], [25], the authors consider the
throughput‑maximization in networks with dynamic • We apply tools from the Lyapunov optimization the‑
lows. More speci ically, in [24], the authors consider a ory to satisfy the time average constraints: through‑
hybrid system with both persistent and dynamic lows. put and power consumption.
They provide a queue‑maximum‑weight based algorithm • The proposed algorithm is proved to provide a solu‑
that guarantees throughput‑optimality while reducing tion arbitrarily close to the optimal.
the latency. In [25], the authors consider a network
with dynamic lows of random size and they arrive in • Simulation results show that our algorithm outper‑
random size at the base station. The service times for forms the baseline algorithm proposed in [3] for
each low varies randomly because of the wireless chan‑ short deadlines and multiple users.

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