Power Management of Base Transceiver Stations for Mobile Networks

A Base Transceiver Station (BTS) is a piece of equipment consisting of telecommunication devices and the air interface of the mobile network. It is referred to as the BS in 3G networks, the eNB in the LTE standard


Introduction
A base transceiver station (BTS) is a piece of equipment consisting of telecommunication devices and the air interface of the wireless network. It is referred to as the BS in 3G networks, the eNB in the LTE standard, and the GNodeB for the 5G. Any wireless service provider operates a country-wide System of BTS. Such a system is the main source of energy consumption with a share in total network consumption greater than 50% (Deruyck et al., 2010), with each BTS absorbing order 10 kW (Lorincz, Garma, & Petrov, 2012). Therefore, system management is expected to investigate methods to reduce the BTS absorbed power. To do that, one may decide to adopt policies to periodically switch off the BTS antennas when they are in an idle state. Such policies, however, are to be sufficiently intelligent not to degrade the BTS quality of service. Indeed, returning an off-antenna to its on-state requires spending a non-negligible amount of time (called setup-time) that makes the BTS slower to respond to customer requests. This may turn into BTS low QoS, such as low response to incoming calls, unsatisfactory VoIP communications, and limited streaming of data (Note 5). Any research in the power management of BTS should thus look at compromises between energy saving and QoS. This paper's aim is to discuss the power management of BTS stations for the best compromise between energy-saving and response to incoming calls.
The paper related works are basically the works (Gandhia, Harchol-Balter, & Adanb, 2010;Harchol-Balter, 2010) and (Gandhia, Gupta, Harchol-Balter, & Kozuch, 2010), and the works , 2014a, 2014b, 2016, and ) that partly overview and synthesize the formers. All these works deal with the power management of server farms and/or data processing systems and give results based on analytical approaches. Since the set of the BTS sectorial antennas can also be seen as a server-farm (where the servers are the BTS antennas), this paper takes the move from all such works, to study the BTS power management. However, the BTS sectorial antennas are aesthetically but not substantially similar to server farms. Indeed, while deriving a server power consumption is quite straightforward, doing the same for an antenna is less immediate, as will be seen in Section 2.1. Moreover, since the analytical approach of the related works suffers from difficulties in mathematically studying various BTS management types in a uniform way (i.e. exact or approximate), by use of simulation this paper may investigate all BTS management types in a uniform way (see Section 3). Even though

BTS modeling
Let us consider the System of BTS stations illustrated in Figure1 (Iazeolla &Pieroni, 2014;, consisting of a series of so-called cells (only 4 System cells are drawn here). Each cell, denoted by S, is served by a central BTS. Let us assume that the confining cells are not overlapping, in other words, that the User Equipments (UE) residing in a given cell S can perform call establishment within only S. Also, assume that each BTS serves the 360° degrees of its area S by 3 sets of antennas (each set is called a set of sectorial-antennas). Each set of sectorial-antennas serves 120° degrees of area S, called a sector, see Figure 2 . Let c be the number of antennas per-sector Figure 2. The three 120° degrees of area S served by the BTS It is assumed that each set of c antennas per sector serves a fixed number of UEs, that we call User Community (UC). In other words, no mobility of UEs is assumed between sectors. Equivalently, it is assumed that there exists a balance of handovers and handoffs between contiguous sectors. A similar assumption holds between contiguous cells. Each cell of the system serves three sectors i.e. three User Communities (UC 1 , UC 2 , UC 3 as illustrated in Figure 2) and each UC i is the source of calls for the c i corresponding antennas.
For each sector i (i = 1, 2, 3) of a given cell, the pair [UC i , c i ] defines queueing system, where UC i is the source of call packets (that we briefly denote as calls) and c i is the number of parallel antennas serving the incoming calls.  Vol. 7, No. 1;2022 For the sake of simplicity, we shall denote by [UC, c] the considered queueing system for any sector i, as illustrated in Figure 3  , where calls waiting to be served are queued in the call queue in front of the c antennas. The queueing model parameters are the arrival-rate λ of calls (number of calls per time-unit) from the source and the antenna-service rate μ. Where λ = 1/E(t a ), with E(t a ) the average call inter-arrival time and μ = 1/ E(t s ) with E(t s ) the antenna average call-service time, or the time each antenna (sometimes here also called a server) takes to serve one call. We shall denote by f(t a ) the density function of the inter-arrival times, with average E(t a ) and with f(t s ) the density function of the service time, with average E(t s ).
The sectorial-antennas average response time E(T) is defined as the total time in which the call remains in the BTS. In other words, the sum of the average waiting_time (spent in the call queue) and the average service_time (spent in the antenna), see Figure 3, where the throughput X denotes the average number of served calls per sec. The sectorial antennas power P is defined as the power absorption of the c antennas during the call service.
Based on such definitions, the following indices (Note 1) are considered: Good performing sectorial-antennas are the ones that ensure low response time E(T) to the incoming calls. In other words, low E(T) is an index of good QoS. On the other hand, as already said and better seen in the paper, the average response time E(T) can be minimized only at the cost of keeping the sectorial antennas always on, and thus at the cost of increasing the average power absorption E(P). So, saving power may turn into a waste of performance, in other words, into a waste of QoS.
Let us denote by the pair (π, δ) the sectorial antennas management strategy, where: • π is the power management policy, or the criterion according to which the antennas are switched between the on, off, or idle state.
• δ the queue-servicing discipline, or the criterion according to which the antennas peak the waiting calls from the call queue when they become idle.
The power management policy π problem derives from the fact that antennas generally operate most of the time at between 10 and 50 percent of their maximum utilization levels (Barroso & Holzle, 2007). So, energy-saving requires avoiding powering the antennas when they are not transmitting. In other words, policies to decide in which state (idle or off) to keep the antennas when not in the on-state (or busy).
In order to save power, one would suggest keeping antennas in the idle or the off state when not busy. However, switching an antenna from the off to the on state implies a time-overhead (the so-called setup-time) with an additional power penalty. Thus, any power-saving policy may result in a time-wasting problem. As a consequence, the BTS may lose performance. This means increased response time to the incoming calls, and low throughput X (served calls/sec), since throughput goes in the inverse way of response time (Kleinrock, 1975;Denning & Buzen, 1978).
This paper's aim is to investigate the BTS power management strategies (π, δ) that yield the best compromise between E(T) and E(P), namely minimum E(P), minimum E(T), and minimum E(PT).
The c antennas are managed according to a given power management policy π. In particular, three policies are considered: 1. The On/Idle policy 2. The On/Off policy 3. The On/Off/stag policy according to terminology introduced in (Gandhi, Harchol-Balter, & Adanb, 2010;Harchol-Balter, 2010).
• In the On/Idle policy the antennas are never turned off. All antennas are either on or idle, and remain in the idle mode when there are no calls to serve. Assuming the system consists of c antennas if an arrival finds an antenna in the idle state it starts service on it. Arrivals that find all c antennas in the on state (i.e. busy) remain in the call queue from which the antennas (when in the idle state) will pick calls.
• The On/Off policy, instead, consists of immediately turning off the antennas when not in use. However, there is a setup time for turning on an off antenna. Under this policy, an antenna is immediately shut down when not in use.
• The On/Off/stag policy operates to maintain to 1 the number of antennas that can be in the setup mode, at any point of time. This limits the setup costs, which are incurred when the antennas are turned on. With this policy, no other antenna can be fired-on if there is one in the setup status.
Two call-queue servicing disciplines δ are considered: 1. The FIFO (First In First Out) discipline, i.e. serve the first arrived call first.
2. The SPTF (Shortest Processing Time First) discipline, i.e. serve the call that requires the shortest processing time first.
We shall further illustrate the effects of such disciplines on the E(T), E(P), and E(PT) indices.

BTS Model Parametrization
The Figure 3 model resembles the queueing model known to the queueing theory as the single-source and k parallel servers model (Kleinrock, 1975). It is denoted (M/M/k) when the density function of the inter-arrival times f(t a ) and the density function of the service time f(t s ) are both exponential (denoted by M). In substance, ( ) = ⋅ ⋅ , and ( ) = ⋅ ⋅ . The model also assumes the queueing discipline δ to be time-independent (i.e. FIFO, LIFO, RAND). All such disciplines have the same effect on the average E(T) and E(P).
The standard M/M/k model assumes the servers (the sectorial antennas in our case) are either in the on or in the idle state, and they remain in the idle state when there are no jobs (i.e. calls) to serve.
Such a behavior, thus, coincides with the above-defined On/Idle policy π. Indeed, under this policy, the antennas are never turned off. They all stay in the idle state and turn in the on-state when there are calls to serve.
If the f(t a ), and the f(t s ) are exponential and the FIFO discipline δ is assumed, the Figure 3 model can be seen as an M/M/c model and then its E(T) (that also gives the one of the On/Idle policy) is expressed by the well-known formula from queueing theory (Kleinrock, 1975): is the probability that there are no jobs (calls) in the system, and where μ = 1/ E(t s ) with E(t s ) being the average service time, or the time a server (antenna) takes to serve a call and ρ is the so-called utilization coefficient, defined To parametrize the model, one can consider that antenna service time E(t s ) consists of the call processing and call transmit time, and can be defined by writing: E(t s ) = Call processing + Call transmit time = Call processing + Call length / antenna bandwidth. E.g., under assumptions (Note 2) such as: Call processing time = 0.9 sec, Call length = 0.5 Mb and Bandwidth = 5Mb/sec one obtains Call transmit time = 0.5/5 = 0.1 sec. From where E(t s ) = 0.9 + 0.1 = 1sec/call, and μ = 1/Et s ) = 1 call/sec.
By denoting P ON as the power the antenna absorbs in the on-state and P IDLE in the idle-state, the average power absorption E(P) is simply obtained by writing: where is the expected number of antennas in the on state, and ( − ) is the expected number of antennas in the idle state.
To obtain P ON and P IDLE we are to look at the antenna operating power. According to (Tombaz S, Vastberg A, and Zander J., 2011) the average power consumption P A of an antenna, can be modeled as a linear function of average radiated power, given by where: • P A is the antenna's total average absorbed power • P TX is the power fed to the antenna to transmit • a accounts for the part of the power consumption that is proportional to the transmitted power (e.g. radio-frequency amplifier power, including feeder losses) . dependent on the traffic load .
• b denotes the average absorbed power that is consumed, independent of average transmit power (e.g. signal processing, site cooling, backhaul transceiver).
One can thus write P ON = P A = a P TX + b and with, according to (Tombaz S, Vastberg A, and Zander J., 2011): where, R cell is cell radius, w is the system bandwidth, β and γ are the path loss coefficients, N 0 is the power spectral density of additive white Gaussian noise, G is the antenna gain and T is the required transmitter power calculated by T=w log 2 (1+γ 0 ) with γ 0 the SNR of the cell edge user (Tombaz, Vastberg, & Zander, 2011). P TX is thus dependent on the system bandwidth w. According to (Tombaz, Vastberg, & Zander, 2011), a typical value for w = 5MHz is P TX =30 Watt and thus by assuming (Note 3) a=3 and b=150 one obtains

The simulation approach
Analytical approaches to the evaluation of the (π, δ) = (On/Idle, FIFO), (On/Off, FIFO) and (On/Off/stag, FIFO) strategies have been thoroughly investigated in Section 1 already referenced papers (Gandhi, Harchol-Balter, & Adanb, 2010;Harchol-Balter, 2010) and (Gandhi, Gupta, Harchol-Balter, & Kozuch, 2010), that deal with server farms. Such papers obtain exact results for the (On/Idle, FIFO) strategy (for the reason that, as seen above, such a strategy can be turned into a standard queuing model of simple evaluation), while only approximate results for the (On/Off, FIFO) and (On/Off/stag, FIFO) strategies (for the reason that they turn into complex Markovian processes, of high time-complexity for an increasing number c of servers).
For this reason and the intention to treat all cases equally with the same method (i.e. both the On/Idle and the On/Off or On/Off/stag, with both the FIFO and the SPTF) and obtain comparable results independently of their process complexity, this paper uses simulation in alternative to the analytical approach.
By use of simulation, this paper may also thoroughly study (see Section 5) the very positive effects of the SPTF call servicing discipline in sectorial antennas, thus overcoming the difficulty (Gupta, Harchol-Balter, Sigman, & Witt, 2007) of analytically studying the SPTF job servicing disciplines in server farms.
The used simulation method was DES, or Discrete Event Simulation (Dannenberg, 2020), which modeled the operation of the BTS as a discrete sequence of events in time. The basic events were the call arrivals at the call queue, and the end-of call-services by the sectorial antennas.
The system random variables that needed to be characterized were the call-interarrival-time and the antenna-service-time. For this purpose, the distribution-driven DES was chosen (in place of the e.g. trace-driven, and program-driven), since of better flexibility. This was accomplished by introducing a set of pseudorandom number generators (Khan, 2016) to simulate the call interarrival times and the antenna service times.
With these principles, first a distribution-based DES simulation model was created. From this, a set of simulation programs was developed by use of the Java programming language. This gave place to a deep simulation system developed in two steps (Scorzini, 2012) and (Iazeolla, Pieroni, & Scorzini, 2013).This system, however, was conceived to study server farms.
It was then completed, again in Java, for the scopes of this paper, to introduce the BTS model parameterization of Section 2.1. This simulation system was then used to obtain the results presented in the following Sections in graphical form. The Java programs produced results in tabular form. These were then translated into the paper graphics by use of Microsoft Excel.
The simulation was carried out by observing the calls residence times T (seen in Figure 3) and the power absorption P of the c antennas in the course of the call services and then averaging the T and P overall observed calls, to obtain E(T) and E(P) at a 90% confidence level.
The Simulation proceeded by first removing the initial bias (which required about 1000 observed calls) and then calculating the E(T) and E(P) confidence intervals by the use of the classic estimator (Iglehart, 1976;Kleijnen, 1975).
To validate the E(T) and E(P) simulation results, these were compared to analytical results coming from formulas (1) and (2)  The simulation studies of Section 4 below deal with the effects of the power management disciplines π with the δ = FIFO call servicing order. The effects of the power management disciplines π with instead the δ = SPTF are studied in Section 5, where it is proven that SPTF plays an important role in the best compromise between energy-saving and response to incoming calls.

Effects of the BTS power management policies π with FIFO
This Section reports the simulation results on the effects of the (On/Off, FIFO), (On/Idle, FIFO), and (On/Off/stag, FIFO) strategies on the BTS response time E(T) and the power consumption E(P). In particular, Sections 4.1 and 4.2 give the graphics of the effects in the case of small setup and high setup times, respectively (the curves reflect the central values of the estimated 90% confidence interval). Section 4.3 then summarizes the effects in the two cases.  For larger values of cρ , instead, a rapid increase of E(T) takes place and tends asymptotically to infinity for cρ tending to 30, i.e. for ρ tending to 1, as analytically predicted from formula (1). In the (On/Off, FIFO ) case, the E(T) shows the so-called bathtub behavior, i.e. higher values of E(T) for small ρ and high ρ. In fact, for small ρ the setup time has a greater influence, since with a lower rate of arrivals the probability that an antenna is turned off (and therefore has to be switched on) is greater, while for high ρ the asymptotic effect predominates as with On/Idle policy. Finally, in the (On/Off /stag, FIFO) case, the almost constant trend for relatively small ρ ( p = cρ < 20) is nothing more than the sum (equal to 2) of E(t s ) =1 and T setup = 1, since with the On/Off/stag policy no other antenna can be fired-on if there is one in the setup status. Consequently, almost all calls experiment both an E(t s ) and a T setup .

Power management policies π with FIFO and small setup time
Again, for the small setup time Figure 4b gives the absorbed power E(P).     Figure 4a for the On/Off (i.e. higher values of E(T) for small ρ and high ρ) and shows that, due to the high setup, the On/Off E(T) turns to be considerably higher than the E(T) with low setup (Figure 4a). So the gap between the On/Off and the On/Idle (not affected by setup) grows in the passage from low setup to high setup. In other words, the distance of the On/Off from the On/Idle is greater in the case with a high setup and, therefore, much higher is the response time with respect to the On/Idle. For the purposes of the low E(T), therefore, in the presence of a high setup time, the On/Idle policy is much more convenient than the On/Off.

Power Management Policies π with FIFO and High Setup Time
Again for the high setup time, Figure 5b gives the absorbed power E(P).

Summary of the Effects of the BTS Power Management Policies π with FIFO
In conclusion, the results of the BTS power management π with FIFO can be synthesized as follows: 1) Effects on the absorbed power E(P) The (On/Idle, FIFO) strategy is the most expensive in terms of energy consumption. Especially with a very low rate of arrivals λ (or, as said, very low cρ), the strategy has a very bad energy yield due to the power consumption of the antennas in the idle state. While as the rate λ of arrivals increases, there are fewer and fewer antennas in that state. With respect to the (On/Idle, FIFO) strategy, the (On/Off, FIFO) consumes less power since the idle antennas are turned off while being penalized by the presence of the setup consumption. The most advantageous strategy for the absorbed power E(P) is the (On/Off/stag, FIFO) having at most 1 antenna in the setup-state. The advantage over the (On/Off, FIFO) is larger in the central part of the graph (medium arrival rates λ), while for high arrival rates the three policies are almost equivalent. Increasing the setup time, the (On/Off, FIFO) strategy considerably reduces the benefits in terms of consumed power. Indeed a long setup involves a waste of energy.

2) Effects on the response time E(T)
Compared with the E(T) On/Idle,FIFO , the E(T) On/Off,FIFO trend tends to have high values for very small and for very high values of cρ. Indeed, for small values, the setup time has a greater impact, since with a lower cρ, i.e. lower rate of arrivals λ, the probability that an antenna is turned off (and therefore has to be turned on) is greater. On the other hand, for high values of cρ, i.e. with a higher rate of arrivals λ, the probability increases that a call will remain in the waiting queue waiting to be processed.
All that above is synthesized in Table 1. The Table (Note 6) shows the effects on the BTS response time E(T) and the power consumption E(P) of the On/Off, On/Idle and On/Off/stag policies, with the δ = FIFO call servicing discipline. It shows that any reduction in power consumption is paid for by an increase in response times.
The next Section evaluates the power management π effects if the δ = SPTF call servicing discipline, rather than FIFO, is used and shows the SPTF large advantages over FIFO on both the E(T) and the E(P).

Effects of the BTS Power Management Policies π with SPTF
Table 1 has shown that, with FIFO, any reduction in power consumption is paid by an increase in response times. So, why not adopt queueing disciplines that minimize the response times? The SPTF job servicing discipline (Shortest Processing Time First) i.e. serving the shortest-to-process job first, is proven in literature (Gupta, Harchol-Balter, Sigman, & Witt, 2007;Conway, Maxwell, & Miller, 1967) to give sensible advantages over FIFO in many contexts. The main advantage of SPTF with respect to FIFO is to minimize the average job waiting time and, correspondently, the job response time.
So, it is appropriate to investigate the advantages the SPTF might bring to the BTS response time (T in Figure 3), where the jobs are the arriving calls, and to the BTS associated parameters P and PT.
To this purpose, for any given (π, δ) strategy, i.e. policy and discipline combination, the following BTS indices will be used to extend the 3 indices introduced in Section 2: 1. P(π, δ), the average power E(P) absorbed by the BTS under the (π, δ) strategy. To be minimized.
Minimizing the PT can be seen as maximizing the performance x Watt, with "performance" being defined as the inverse of the mean response time (Gandhi, Gupta, Harchol-Balter, & Kozuch, 2010), i.e. the call-throughput X (or BTS served calls/sec) in Figure 3. Indeed, as already said, it is known (Kleinrock, 1975;Denning & Buzen, 1978) that the smaller the mean response time T, the higher the throughput X.
Section 4 above has shown the effects of the δ = FIFO discipline on E(P) and E(T) for increasing values of p = cρ, in other words for increasing values of ρ, the BTS utilization coefficient, from 0 to 1.
Low ρ meaning low BTS load, i.e. very few calls in the waiting queue ( Figure 3) and high ρ many calls in the queue. However the δ =SPTF proceeds by extracting the shortest-to-process calls first from the queue. So to be competitive with δ =FIFO it has to find more than just a few calls in the queue. Therefore in this Section, we will not study the effects of the δ = SPTF discipline on E(P) and E(T) for increasing values of ρ (so we'll not present graphics). We will only study two typical BTS loads, (low ρ (ρ= 0.5, i.e. cρ = 15 ) and high ρ (ρ→1, specifically ρ = 0.97, i.e. cρ = 29)). However non to neglect the effects of the policy π, we will remain experimenting with the study of the BTS setup time T setup . So, the two typical setup times (T setup = 1sec and T setup = 10sec) are still considered in Sections 5.1 and 5.2 below, along with the δ = SPTF queueing discipline.
Below we shall not consider the On/Off/stag policy (Note 4) studied in Section 4 and will limit the study to the On/Off and On/idle under different queueing disciplines δ. Consequently, only the following four (π, δ) strategies are investigated:
Simulation results are shown in the following Sections, where they prove that the optimal PT (i.e. minimum response time x Watt, or maximum throughput x Watt) is obtained with the discipline δ = SPTF rather than with the FIFO, whichever is (On/Off or On/Idle) the policy π!
Results also prove that, in some circumstances, to reduce BTS response time E(T) (i.e. increase the BTS throughput X) it is better to operate on the queueing discipline δ than on the server policy π. And vice versa in some other circumstance!
In particular, in the low setup case (see the below discussion on Table 2), it is better to move from δ=FIFO to δ = SPTF, rather than from π = On/Off policy to π = On/Idle. But vice versa in the high setup case (see the below discussion on Table 3). • Seeing at the power consumption P, one notes that for low ρ there is no effect on P coming from the queueing discipline δ, while there is an effect from the policy π. In fact P(On/Idle,FIFO) = P(On/Idle, SPTF) = 6000 W, and P(On/Off, FIFO) = P(On/Off, SPTF) = 4273.

Power Management Policies π with SPTF and Low Setup Time
The drastic reduction (from 6000 W to 4273 W, for low ρ) from On/Idle to On/Off, takes place since, when ρ is low, the call queue is almost empty and thus a large number of antennas is in the off state. For high ρ instead, the power consumption P remains practically unchanged (P = around 7100 W) both with the policy π (i.e. no effect by the low setup time), and with the discipline (the queue is always full and thus the antennas remain always in the on state).
• Seeing at the response-time T, one can first note what was said above, i.e. that the positive effect of the SPTF discipline (i.e. lower T than with FIFO, specifically 1.3 instead than 1.8 and 1.35 instead than 2) is seen when there are many calls in the queue, i.e. with a high . Moreover, can note that there is an effect on T both by the queueing discipline and by the policy. The effects hold both for low ρ and for high ρ. In the On/Idle case, when ρ is low, there is no waiting in the call-queue and thus the mean response time T is of about the mean call service time (E(t s ) = 1 sec) while it increases (T = 1.8sec for δ = FIFO and T = 1.3sec for δ = SPTF) for high ρ, but in a lower measure for SPTF due to the SPTF property of minimizing the average response time E(T).
In the On/Off case, when ρ is low, the mean response time is higher (T = 1.2 sec instead than 1) since almost every arrival finds the antennas in the off state, and thus every call incurs in the setup time (however with no effects by the discipline, since the queue is empty). For high ρ, instead, the mean response time increases (from 1.2 to 2 sec for δ = FIFO and from 1.2 to 1.35 sec for δ = SPTF) due to the large queueing, again in a lower measure for SPTF.
As predicted above, one can see that the reduction in response-time obtained moving from FIFO to SPTF is larger than when moving from On/Off to On/Idle. Indeed (see high ρ) moving from (On/Off, FIFO) to (On/Idle, FIFO) the response time T changes from 2 to 1.8 (a 10% reduction). Moving, instead, from the (On/Idle, FIFO) to the (On/Idle, SPTF) the response time T changes from 1.8 to 1.3 (an almost 30% reduction).
• Seeing at the PT index, its values are a consequence of the P and the T ones. Table 2 shows that in the low setup case the optimal PT (i.e. minimum response time x Watt, or maximum throughput x Watt) is obtained, when ρ is low, only with the π = (On/Off) policy, whichever is the discipline δ. While, for high ρ, the optimal PT is obtained only with δ = SPTF, whichever is the policy π. Table 3 reports the simulation results (Note 6) in the high setup case (T setup = 10sec). • Seeing at the power consumption P, one notes that for low ρ there is no effect on P coming from the queueing discipline δ, while there is an effect from the policy π. In fact P(On/Idle,FIFO) = P(On/Idle, SPTF) = 6000 W, and P(On/Off, FIFO) = P(On/Off, SPTF) = 5634. The reduction (from 6000W to 5634W, for low ρ) from On/Idle to On/Off, takes place since, when ρ is low, the call-queue is almost empty and thus a large number of antennas is in the off state.

Power Management Policies π with SPTF and High Setup Time
For high ρ instead, the power consumption P shows no change from the discipline δ (since the queue is always full and thus the antennas remain always in the on state) but some changes from the policy π (from 6956 on/idle to 7116 on/off) by the effect of the high setup time • Seeing at the response-time T, one first notes what was said above, i.e. that the positive effect of the SPTF discipline (i.e. lower T than with FIFO, specifically 1.3 instead than 1.8 and 2.6 instead than 3.6) is seen when there are many calls in the queue, i.e. with a high .
Moreover, one notes that there is an effect on T both by the queueing discipline and by the policy. The effects hold both for low ρ and for high ρ. In the On/Idle case, when ρ is low, there is no waiting in the call-queue and thus the mean response time T is of about the mean job service time (E(t s ) = 1 sec) while it increases (T = 1.8sec for δ = FIFO and T = 1.3sec for δ = SPTF) for high ρ, again for the property of the SPTF.
In the On/Off case, when ρ is low, the mean response time is higher (T = 1.7 sec instead than 1sec) since almost every arrival finds antennas in the off state, and thus every job incurs in the setup time (however with no effect by the discipline, since the queue is empty). For high ρ, instead, the mean response time increases (from 1.7 to 3.6 sec for δ = FIFO and from 1.7 to 2.6 sec for δ = SPTF) due to the large queueing. At the opposite of the low setup case, with the high setup now the reduction in response-time one may obtain moving from FIFO to SPTF is smaller than the one when moving from On/Off to On/Idle. Indeed (see high ρ) moving from (On/Off, FIFO) to (On/Idle, FIFO) the response time T changes from 3.6 to 1.8 (a 50% reduction). Moving, instead, from the (On/Idle, FIFO) to the (On/Idle, SPTF) the response time T changes from 1.8 to 1.3 (a 30% reduction).
• Seeing at the PT index, its values are a consequence of the P and the T ones. Opposite to the low setup case (Table 2), the high setup case of Table 3 shows that the optimal PT (i.e. minimum response time x Watt, or maximum throughput x Watt) is obtained, for low ρ, only with the π = (On/Idle) policy, whichever is the discipline δ. While, for high ρ, only with δ = SPTF, whichever is the policy . 

Summary of the effects of the BTS power management policies π with SPTF
In summary, the effects of the BTS discipline management δ = SPTF can be synthesized as follows: • In the low setup case, the optimal (i.e. minimal) PT is obtained, when ρ is low, only with the π = (On/Off) policy, whichever is the discipline δ. While, for high ρ, only with the discipline δ = SPTF, whichever is the policy .  • In the high setup case the optimal (i.e. minimal) PT is obtained, for low ρ, only with the π = (On/Idle) policy, whichever is the discipline δ. While, for high ρ, only with the discipline δ = SPTF, whichever is the policy π.
In substance, both in the low and the high setup case, the SPTF discipline ensures the best PT (i.e. minimal response time x Watt). In other words the best compromise between energy-saving and QoS (all that may affect the cost / benefit ratio of wireless services such as response to incoming calls, VoIP communications and streaming of data (Note 5).

Conclusion
Any wireless service provider operates a country-wide System of Base Transceiver Stations (BTS). Such a System is the main source of energy consumption with a share in total network consumption greater than 50%. Therefore, system management is expected to investigate methods to reduce the BTS absorbed power. To do that, one may decide to adopt policies to periodically switch off the BTS antennas when they are in an idle state. Such policies, however, are to be sufficiently intelligent not to degrade the QoS of the BTS.
To this scope, this paper has studied the combined effect of the BTS policy π (or criterion according to which the BTS antennas are switched between the On, Off, or Idle state) and of the BTS queueing discipline δ (or the criterion according to which the BTS antennas serve calls: FIFO or SPTF, i.e. serve the first arrived call first. or serve the shortest-to-process call first). The paper simulation results prove that: 1) Whichever is the policy (On/Off, or On/Idle), if the δ = FIFO discipline is used, any reduction in power consumption P is paid by an increase in response times T, i.e. is paid by a reduction of QoS (low response to incoming calls, unsatisfactory VoIP communications and limited streaming of data (highly compromised by long delays T).
2) Whichever is the policy (On/Off, or On/Idle) if the δ = SPTF discipline is used, one obtains the best compromise between power consumption P and QoS. In other words the best PT, or BTS performance x Watt, i.e. minimum response time T per consumed power P. That means minimum power consumption to obtain a quick response to incoming calls, satisfactory VoIP communications and good streaming of data.
The distribution-driven DES method (Discrete Event Simulation) has been used to build a simulation model. From this, a set of simulation programs, developed in Java programming language, has given place to a deep simulation system used to obtain the paper results. All simulation results were validated by comparison to mathematical models.